The NASA-UC Eta-Earth Survey by the California Planet Search (CPS) group is a systematic search for low-mass planets (~3-30 Earth masses) orbiting the nearest 230 GKM stars suitable for high-precision Doppler observations at Keck Observatory. These 1 m/s radial velocity measurements of a well-defined sample of nearby stars will provide one the first estimates of the fraction of stars with Earth-like planets. This talk will describe the Eta-Earth Survey and other searches for low-mass planets. It will focus on recently announced super-Earths and Neptune-mass planets from the Eta-Earth Survey, including HD 7924b, a 9.3 Earth mass (Msini) planet in a 5.4 day orbit. These low- mass planets are extraordinarily valuable in their own right, as targets for transit and other follow-up studies, and as windows into the mechanisms of planet formation.