This chapter is devoted to the recently defined concept of strongly regular signed graphs (SRSGs), which generalizes the notion of strongly regular graphs from the domain of ordinary graphs. It presents the basic properties of SRSGs, provides specific constructions, and, as a fundamental result, classifies them into five disjoint classes. Each class is examined in detail, highlighting both similarities and distinctions with strongly regular graphs. The chapter also explores particular connections with 3-class association schemes, as well as constructions of signed Johnson and signed Hamming graphs. The concept of strong regularity is further combined with net regularity and walk regularity, with particular attention given to signed graphs that belong to the intersection of these classes. SRSGs with a small number of eigenvalues are analysed, accompanied by numerous illustrative constructions. For example, it has been shown that every connected signed graph with exactly two eigenvalues must be strongly regular.