For the investigation of chemical reaction networks, the identification of all relevant intermediates and elementary reactions is mandatory. Many algorithmic approaches exist that perform explorations efficiently and in an automated fashion. These approaches differ in their application range, the level of completeness of the exploration, and the amount of heuristics and human intervention required. Here, we describe and compare the different approaches based on these criteria. Future directions leveraging the strengths of chemical heuristics, human interaction, and physical rigor are discussed.