Wireless acoustic sensor networks (WASNs) are formed by a distributed group of acoustic-sensing devices featuring audio playing and recording capabilities. Current mobile computing platforms offer great possibilities for the design of audio-related applications involving acoustic-sensing nodes. In this context, acoustic source localization is one of the application domains that have attracted the most attention of the research community along the last decades. In general terms, the localization of acoustic sources can be achieved by studying energy and temporal and/or directional features from the incoming sound at different microphones and using a suitable model that relates those features with the spatial location of the source (or sources) of interest. This paper reviews common approaches for source localization in WASNs that are focused on different types of acoustic features, namely, the energy of the incoming signals, their time of arrival (TOA) or time difference of arrival (TDOA), the direction of arrival (DOA), and the steered response power (SRP) resulting from combining multiple microphone signals. Additionally, we discuss methods not only aimed at localizing acoustic sources but also designed to locate the nodes themselves in the network. Finally, we discuss current challenges and frontiers in this field.