Electric fish have evolved multiple times within the bony fish lineage, exhibiting an impressive array of differences with respect to the characteristics of their electric organs. These differences include voltage, waveform, and the underlying cellular and molecular mechanisms of electrogenesis. Here, we describe the diversity and evolution of electric fish with particular attention to the evolutionary transitions that have led to changes in electric organ discharge (EOD) waveforms. We start by reviewing the basic principles of electrogenesis and the structure of electric organs. We then describe the diversity of electric fish EOD waveforms, summarizing what is currently known about the neural control of these signals. We finish with a discussion of the evolutionary transitions that have led to changes in EOD waveform and their potential functional significance.