Noninvasive imaging of cardiac excitation using body surface potential mapping (BSPM) data and inverse procedures is an emerging technique that enables estimation of myocardial depolarization and repolarization. Despite numerous reports on the possible advantages of this imaging technique, it has not yet advanced into daily clinical practice. This is mainly due to the time consuming nature of data acquisition and the complexity of the mathematics underlying the used inverse procedures. However, the popularity of this field of research has increased and noninvasive imaging of cardiac electrophysiology is considered a promising tool to complement conventional invasive electrophysiological studies. Furthermore, the use of appropriately designed electrode vests and more advanced computers has greatly reduced the procedural time. This review provides descriptive overview of the research performed thus far and the possible future directions. The general challenges in routine application of BSPM and inverse procedures are discussed. In addition, individual properties of the biophysical models underlying the inverse procedures are illustrated.