The CDF collaboration has recently completed a set of precision measurements of the top quark mass in 350 pb-1 of data. We describe the strategies used to extract the maximal information from each top quark candidate event, and present the best single measurements in both lepton+jets and dilepton decay channels. We present a combination of these results with measurements from D0 and with previous data from both experiments. The impact of this level of precision on electroweak fits to the Higgs mass, the prospects for future improvements, and the consequences for Higgs and SUSY searches are discussed.