Philosophical musings that other worlds might exist date back more than 2000 years to the ancient Greeks. We live in a fortunate time, when the discovery of exoplanets has the potential to address questions about how planetary systems form and evolve. In what ways do exoplanetary systems mirror our solar system? How are they different? Does the presence of a binary star affect planet formation? Are Earth analogs common? Does the energy from other stars give rise to life?

Confirmed and candidate exoplanets number in the thousands and search techniques include Doppler measurements, transit photometry, microlensing, direct imaging, and astrometry. Each detection technique has some type of observational incompleteness that imposes a biased view of the underlying population of exoplanets. In some cases, statistical corrections can be applied. For example, transiting planets can only be observed if the orbital inclination is smaller than a few degrees from an edge-on configuration. However, with the reasonable assumption of randomly oriented orbits, a geometrical correction can be applied to determine the occurrence rate for all orbital inclinations. In other cases, there is simply no information about the underlying population and it is not possible to apply a meaningful correction. For example, the number of planets with a similar mass (or radius) and a similar intensity of intercepted stellar flux as our Earth is not secure at this time because the number of confirmed detections for this type of planet is vanishingly small.

As a result of the sample biases and observational incompleteness for each discovery technique, our view of exoplanet architectures is fuzzy at best. There are no cases beyond the solar system where the entire parameter space for orbiting planets has been observed. Instead, we piece together an understanding of exoplanet architectures by counting planets in the regimes where techniques are robust and then we estimate correction factors when possible. When drawing conclusions about the statistics of exoplanets, it is helpful to understand completeness in this underlying patchwork of orbital parameter space.

We begin by reviewing the exoplanet detection techniques with particular consideration of the observational biases and then discuss the implications for planet formation with an eye toward how our solar system compares.