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Seismicity declustering, the process of separating the seismicity catalog into foreshocks, mainshocks, and aftershocks, is widely used in seismology, in particular for seismic hazard assessment and in earthquake prediction models. There are several declustering algorithms that have been proposed over the years. Up to now, most users have applied either the algorithm of Gardner and Knopoff (1974) or Reasenberg (1985), mainly because of the availability of the source codes and the simplicity of the algorithms. However, declustering algorithms are often applied blindly without scrutinizing parameter values or the result. In this article we present a broad range of algorithms, and we highlight fundamentals of seismicity declustering and possible pitfalls. For most algorithms the source code or information regarding how to access the source code is available on the CORSSA website.