There are a number of techniques for trying to discover planets around stars; these include the astrometric methods, radial velocities, transits, and direct observations. There have been many attempts, and even announcements of success, to discover planets based on astrometric observations. The astrometric method has discovered many double star systems. The discoveries are related to the accuracy of the observations, the distance to the star, the relative mass of the secondary body, the orbital period of the planet, and the length of the observational period. The Hipparcos satellite significantly improved the accuracy of the observations, but suffered from a short observing period. It discovered double stars, but not any planets. The results of the Hipparcos proper motion determinations are a good indication of future possibilities, ranging from double star determinations to indications of problems with solutions. The radial velocity technique has been applied very successfully to discover planets, and the results are a variety of different types of solar systems, limited by the selection effect imposed by the observational capabilities. The transit technique has the ability to detect much smaller planets and has had limited success to date. The direct observation of planets from space by means of coronographic techniques and interferometer nulling is under consideration. The advent of optical interferometers on the ground and the promise of future space systems makes the prospects for future astrometric discoveries bright. The SIM, GAIA, and maybe TPF missions have the accuracy for possible detection of planets. The analyses of the positional observations can have a variety of results for the proper motions, including the presence of periodic motions, non-linear motions, stochastic variations, or larger than usual residuals. This can result in the discovery of planets, the need for further observations, or the requirement for more accurate instrumentation. The possible presence of multiple planets around a star requires solution methods that can determine multiple, varied amplitude periodicities in the presence of noise in the observations.