Constraints on the ambient (circumsolar) interstellar medium can be derived from observations of interstellar neutrals or their derivatives in the heliosphere. New results have been recently obtained which, when combined with optical and UV observations of the nearby stars (HST-GHRS, EUVE), remove long-standing contradictions and allow us to infer for our local cloud, pressure, ionization and limits on the magnetic field. The electron density in the circumsolar gas is found to be between 0.04 and 0.15 cm−3. Its total thermal pressure is within the interval 1700 – 2600 cm−3 K. If the local magnetic field is nearly perpendicular to the interstellar wind flow, which is likely, then its intensity is smaller than 3.6 μG. Our Sun is located very close to the edge of the local cloud (the volume of gas which has the same physical properties as the circumsolar gas), while there are at least 5 other cloudlets within 10 pc. Abundances vary from cloudlet to cloudlet. How they are located and whether they are separated by tenuous gas or shock discontinuities is not clear yet. Semi-hot (105 K) gas has been detected in absorption towards nearby stars (Wood et al, 1996), which probably originates in the “H walls” surrounding our heliosphere and other asterospheres. This shows that semi-hot gas is not necessarily linked with cloud interfaces with the hot gas of the Local Bubble.