The field of electrocardiography has been in existence for over a century, yet despite significant advances in adult clinical electrocardiography, signal processing techniques and fast digital processors, the analysis of fetal ECGs is still in its infancy. This is, partly due to a lack of availability of gold standard databases, partly due to the relatively low signal-to-noise ratio of the fetal ECG compared to the maternal ECG (caused by the various media between the fetal heart and the measuring electrodes, and the fact that the fetal heart is simply smaller), and in part, due to the less complete clinical knowledge concerning fetal cardiac function and development. In this paper we review a range of promising recording and signal processing techniques for fetal ECG analysis that have been developed over the last forty years, and discuss both their shortcomings and advantages. Before doing so, however, we review fetal cardiac development, and the etiology of the fetal ECG. A selection of relevant models for the fetal/maternal ECG mixture is also discussed. In light of current understanding of the fetal ECG, we then attempt to justify recommendations for promising future directions in signal processing, and database creation.