The fetal electrocardiogram (fECG) was first recorded from the maternal abdominal surface in the early 1900s. During the past fifty years, the most advanced electronics technologies and signal processing algorithms have been used to convert noninvasive fetal electrocardiography into a reliable technology for fetal cardiac monitoring. In this chapter, the major signal processing techniques, which have been developed for the modeling, extraction and analysis of the fECG from noninvasive maternal abdominal recordings are reviewed and compared with one another in detail. The major topics of the chapter include: 1) the electrophysiology of the fECG from the signal processing viewpoint, 2) the mathematical model of the maternal volume conduction media and the waveform models of the fECG acquired from body surface leads, 3) the signal acquisition requirements, 4) model-based techniques for fECG noise and interference cancellation, including adaptive filters and semi-blind source separation techniques, and 5) recent algorithmic advances for fetal motion tracking and online fECG extraction from few number of channels.