Computing subgraph frequencies is a fundamental task that lies at the core of several network analysis methodologies, such as network motifs and graphlet-based metrics, which have been widely used to categorize and compare networks from multiple domains. Counting subgraphs is however computationally very expensive and there has been a large body of work on efficient algorithms and strategies to make subgraph counting feasible for larger subgraphs and networks. This survey aims precisely to provide a comprehensive overview of the existing methods for subgraph counting. Our main contribution is a general and structured review of existing algorithms, classifying them on a set of key characteristics, highlighting their main similarities and differences. We identify and describe the main conceptual approaches, giving insight on their advantages and limitations, and provide pointers to existing implementations. We initially focus on exact sequential algorithms, but we also do a thorough survey on approximate methodologies (with a trade-off between accuracy and execution time) and parallel strategies (that need to deal with an unbalanced search space).