The purpose of this review is to provide a survey of some of the most important bifurcation phenomena that one can observe in pulse-modulated converter systems when operating with high corrector gain factors. Like other systems with switching control, electronic converter systems belong to the class of piecewise-smooth dynamical systems. A characteristic feature of such systems is that the trajectory is “sewed” together from subsequent discrete parts. Moreover, the transitions between different modes of operation in response to a parameter variation are often qualitatively different from the bifurcations we know for smooth systems. The review starts with an introduction to the concept of border-collision bifurcations and also demonstrates the approach by which the full dynamics of the piecewise-linear, time-continuous system can be reduced to the dynamics of a piecewise-smooth map. We describe the main bifurcation structures that one observes in three different types of converter systems: (1) a DC/DC converter; (2) a multi-level DC/DC converter; and (3) a DC/AC converter. Our focus will be on the bifurcations by which the regular switching dynamics becomes unstable and is replaced by ergodic or resonant periodic dynamics on the surface of a two-dimensional torus. This transition occurs when the feedback gain is increased beyond a certain threshold, for instance in order to improve the speed and accuracy of the output voltage regulation. For each of the three converter types, we discuss a number of additional bifurcation phenomena, including the formation and reconstruction of multi-layered tori and the appearance of phase-synchronized quasiperiodicity. Our numerical simulations are compared with experimentally observed waveforms.