An overview is presented of tests performed to check the statistical properties of the formal errors on the Hipparcos parallaxes. It is shown that there is no evidence for systematic or correlated errors beyond a correlation level of 0.12 and an angular scale of 1.2 degrees.

The Hipparcos astrometry is used mainly for the derivation of stellar physical quantities such as luminosity, masses and velocity. However, sample selections on data with observational errors or an intrinsic dispersion may lead to biased estimates, especially when the error distributions are non-Gaussian. We review the classical biases and the ways to avoid them through the use of statistical methods.

In the context of the luminosity calibration of the nearer stars I discuss the Hipparcos results on distances to nearby OB associations and open clusters. The shortcomings and assumptions in the analyses used to derive these results are pointed out and for the open clusters a comparison is made with results obtained from main sequence fitting. I conclude that given the considerable uncertainties in the latter technique there is no convincing evidence that the Hipparcos based distances to open clusters beyond the Hyades should not be trusted.

Hipparcos provided us with valuable observational material that can be used to anchor more firmly the Galactic and extragalactic distance scales. A calibration which is applicable to all stars must allow for differences in chemical composition and other properties, which may require the use of theoretical models. I discuss some difficulties encountered in the calibration procedure that are related (1) to the determinations of stellar temperatures, luminosities and chemical compositions, (2) to remaining weaknesses of theoretical stellar models, and (3) to the transformations of the model outputs from the (Mbol, Teff) plane into any colour-magnitude or colour-colour diagram.

The HIPPARCOS satellite has provided astronomy with a wonderful legacy. We now have high-quality parallaxes for some of the yellow and red giants as well as for some of the A and F main sequence standards. It is now possible to compare field giants with those in globular clusters and to resolve some of the discrepancies. Hipparcos luminosities are being compared with various existing MK calibrations and the most glaring (i.e. interesting) inconsistencies will be discussed.

Recent results are reviewed for two methods of luminosity calibration based on high-resolution spectroscopy. The first relies on Teff/log g determinations from model-atmosphere analyses based on high-resolution spectra. This method is physically well founded but operationally demanding, and requires advance knowledge of stellar mass. The second, W-B, stems from the empirical relationship between luminosity and the width of chromospheric emission lines first established by Wilson and Bappu. Its physical basis is only partially understood, however, and the calibration depends on stellar metallicity and on the choice of lines.

Both Teff/log g and W-B easily distinguish cool dwarfs from cool giants. Generally reasonable agreement is found between distances derived from Hipparcos parallaxes and those inferred from the log g values derived for nearby dwarfs with relatively well-known Hipparcos parallaxes, σ(π)/π < 0.2. Constraining Hipparcos parallaxes star-by-star is not possible at present. Improvements are suggested for both approaches.

The Hipparcos parallaxes allow us to revisit photometric calibrations in terms of Mv and to evaluate the effects of the overall metallicity across the HR-diagram. For evolved stars the spread in mass remains the major and irreducible source of errors in the photometric Mv. If the relative locations of open cluster main-sequences are fully explained by the ∆Mv versus ∆[M/H] relation, the residual scatter in the lower main sequence appears due to additional parameters such as rotation or gravitational settling of the heavy elements. These cannot readily be studied by a purely photometric approach.

The ESA HIPPARCOS satellite has provided astrometry of unprecedented accuracy, allowing us to reassess, improve and refine the pre-Hipparcos luminosity calibrations. We review the “classical” absolute magnitude calibrations with the Strömgren-Crawford intermediate-band photometric system. A small zero point correction of about 2-4% seems necessary, as well as to refine the dependences on metallicity and projected rotational velocity. The need of a rigorous statistical treatment of the extremely precise Hipparcos data to derive definitive dependences of the luminosity on physical parameters is emphasized.

The ideal distance indicator would be a standard candle abundant enough to provide many examples within reach of parallax measurements and sufficiently bright to be seen out to Local Group galaxies. The red clump stars closely match this description. These are the metal rich equivalent of the better known horizontal branch stars, and their brightness dispersion is only 0.2 mag (one sigma) in the Solar neighborhood. Using Hipparcos to calibrate a large, local sample, the red clump method has been used to measure accurate distances to the Galactic center (Paczyński & Stanek 1998), M31 (Stanek & Garnavich 1998), LMC (Udalski et al. 1998; Stanek et al. 1998; Udalski 1999) and some clusters in our Galaxy (e.g. 47Tuc: Kaluzny et al. 1998). As with all the distance indicators, the main worry lies in the possible systematics of the method, in particular, the brightness dependence on the stellar metallicity and age. These dependences have come under close scrutiny and, indeed, the population effects on the red clump brightness appear small and calibratable. Perhaps the most controversial result from the red clump method is the estimation of a “short” distance to the Large Magellanic Cloud (Udalski et al. 1998; Stanek, Zaritsky & Harris 1998; Udalski 2000). This distance to the LMC is shorter by 12% than the “standard” value, and has very important implications for the Cepheid distance scale and the determination of the Hubble constant.

Variations of ~ 0.4 mag are expected in the I-band absolute magnitude of red clump giants, , as a function of both stellar age and metallicity. This is the case regardless of some potential theoretical uncertainties. The quite large differences in mean ages and metallicities of clump stars among galaxies result in systematic changes (of up to ~ 0.4 mag) in their . These numbers also indicate a distance to the LMC that is not necessarily “short”.

Asteroseismology involves using the resonant frequencies of a star to infer details about its internal structure and evolutionary state. Large efforts have been made and continue to be made to measure oscillation frequencies with both ground- and space-based telescopes, with typical precisions of one part in 103–104. However, oscillation frequencies are most useful when accompanied by accurate measurements of the more traditional stellar parameters such as luminosity and effective temperature. The Hipparcos catalogue provides luminosities with precisions of a few percent or better for many oscillating stars. I briefly discuss the importance of Hipparcos measurements for interpreting asteroseismic data on three types of oscillating stars: δ Scuti variables, rapidly oscillating Ap stars and solar-like stars.

I briefly review recent observations, some related physics and modelling, and future possibilities relating to our knowledge of the strength, structure and evolution of extragalactic magnetic fields.

We have studied the fate of initial magnetic fields in the hot halo gas out of which the visible parts of galaxies form, using three-dimensional numerical MHD-experiments. The halo gas undergoes compression by several orders of magnitude in the subsonic cooling flow that forms the cold disk. The magnetic field is carried along and is amplified considerably in the process, reaching μG levels for reasonable values of the initial ratio of magnetic to thermal energy density.

A very brief review is given of processes that may be responsible for the generation of initial seed magnetic fields in the early Universe, and that can amplify those fields to the levels observed in galaxies in the current epoch.

Magnetic fields are anchored in gas clouds. Field lines are tangled in spiral arms, but highly regular between the arms. The similarity of pitch angles between gaseous and magnetic arms suggests a coupling between the density wave and the magnetic wave. Observations of large-scale patterns in Faraday rotation favour a dynamo origin of the regular fields. Fields in barred galaxies do not reveal the strong shearing shocks observed in the cold gas, but swing smoothly from the upstream region into the bar. Magnetic fields are important for the dynamics of gas clouds, for the formation of spiral structures, bars and halos, and for mass and angular momentum transport in central regions.

Models of the magnetic field configuration of the Milky Way are reviewed. Current analyses of rotation measure data suggest that the Milky Way possesses a bisymmetric-like spiral magnetic field, that field reversals among spiral arms exist, and that the magnetic spiral may not closely match the mass spiral structure. Zeeman measurements of OH masers may provide alternative magnetic field information.

Of all the methods available to observe magnetic fields in the Milky Way, the mapping of linear polarization at cm wavelengths has proven to be most successful. The instruments that have contributed most of the new data are the 100 m Effelsberg telescope and the Parkes 64 m dish. Their Galactic plane surveys gave us a new conception of the linear polarization distribution. A new Effelsberg 1.4 GHz ‘medium latitude polarization survey’ now being made gives us data about large sections of the Galaxy. Polarization maps of selected regions of the Galaxy are now being made at several frequencies up to 32 GHz. Data from Westerbork at ∼ 325 MHz, as well as data from the Canadian Galactic Plane Survey (CGPS) at 1.4 GHz give new exciting information.

Radio data of large irregular galaxies reveal some extended synchrotron emission with a substantial degree of polarization. In the case of NGC 4449 strong galaxy-scale regular magnetic fields were found, in spite of the lack of ordered rotation required for the conventional dynamo action. The rigidly rotating large irregular NGC 55 shows vertical polarized spurs connected with a network of ionized gas filaments. Small dwarf irregulars show only isolated polarized spots.

There is a broad agreement between the predictions of galactic dynamo theory and observations; although there are still some unresolved difficulties, the theory appears to be robust. Now attention is turning from generic models to studies of particular features of the large-scale magnetic fields, and also to models for specific galaxies. The effects of noncircular flows, for example driven by the interaction of spiral arms and galactic bars with the dynamo, are of current interest.