Global Positioning System (GPS) is widely used in navigationmeasurementemergency communication and other fields.In recent yearsthe scholars are making increasingly intensive researches on acquisition and tracking process of GPS baseband signals.Thereforedifferent acquisition and tracking algorithms are systematically summarized for comparison.According to the processing mode after the mixing of digital Intermediate Frequency (IF) signals with local signalsthe acquisition algorithms can be mainly classified as coherent acquisitionincoherent acquisition and differential coherent acquisitionand a comparison is conducted.According to the function of tracking loopsthe tracking algorithms can be classified as carrier tracking and code loop trackingand a comparison is conducted.The improvements on those acquisition and tracking algorithms in recent years are summarizedand the advantages and disadvantages of the improved algorithms are analyzed.Finallythe prospect of baseband signal acquisition and tracking algorithms is given.