We currently know of close to 800 extrasolar planets orbiting a variety of different host stars. These stars almost always represent the only visible component in the system, they are the dominant energy source for the orbiting planets, and they influence every aspect of planetary physics and evolution. Most astrophysical parameters of extrasolar planets are actually functions of equivalent stellar parameters, whose values are not always accurately known, especially for low-mass stars. The importance of "understanding the parent stars" cannot be overstated in the quest of exoplanet exploration. I present our ongoing interferometric survey of particularly late-type exoplanet host stars with the aim of directly determining stellar radii and related astrophysical parameters. I discuss implications of our results and elaborate on a few particularly interesting systems, such as the low-mass host of a transiting hot Neptune GJ 436b, and the multi-planet systems GJ 581, 55 Cnc, and GJ 876.