Time-to-digital converters (TDCs) are high-performance mixed-signal circuits capable of timestamping events with sub-gate delay resolution. As a result of their high-performance, in recent years TDCs were integrated in complementary metal-oxide-semiconductor (CMOS) technology with highly sensitive photodetectors known as single-photon avalanche diodes (SPADs), to form digital silicon photomultipliers (dSiPMs) and SPAD imagers. Time-resolved SPAD-based sensors are capable of detecting the absorption of a single photon and timestamping it with picosecond resolution. As such, SPAD-based sensors are very useful in the field of biomedical imaging, using time-of-flight (ToF) information to produce data that can be used to reconstruct high-quality biological images. Additionally, the capability of integration in standard CMOS technologies, allows SPAD-based sensors to provide high-performance, while maintaining low cost. In this paper, we present an overview of fundamental TDC principles, and an analysis of state-of-the-art TDCs. Furthermore, the integration of TDCs into dSiPMs and SPAD imagers will be discussed, with an analysis of the current results of TDCs in different biomedical imaging applications. Finally, several important research challenges for TDCs in biomedical imaging applications are presented.