The most common type of defect with which babies are born is related to heart, nearly 1 out of every 100. A physician studies the electrical activity of the fetus's heart, by monitoring the fetal Electrocardiogram (fECG) collected at the time of pregnancy from mother's abdomen. Even though the signal acquisition and signal processing techniques has been made a great deal of progress, the extraction and analysis of Fetal ECG is still in its outset. Very low signal-to-noise ratio of the fetal ECG compared to the maternal ECG, is the biggest challenge faced by scientists working in this area. In this paper, we have reviewed a wide range of signal processing techniques for the extraction of fetal ECG, along with their shortcomings and advantages.