In this chapter, we adapt two concepts from the theory of ordinary graphs to the setting of signed graphs. A signed graph is called integral if its spectrum consists entirely of integers. Two signed graphs are said to be cospectral if they are switching non-isomorphic yet share the same spectrum. In both cases, the term ‘spectrum’ refers to the eigenvalues of a prescribed matrix associated with the signed graph. Integral signed graphs are studied within the class of graphs with vertex degree at most four, with a complete classification provided for those with degree at most three. Numerous sporadic constructions of cospectral signed graphs are considered, alongside two basic operations transferred from the domain of ordinary graphs: GM-switching and WQH-switching, both of which produce signed graphs with identical spectra. As a central result, a pivotal and distinguishing construction is presented that consistently generates cospectral signed graphs, representing a fundamental phenomenon unique to the domain of signed graphs. A survey of signed graphs that do not have a cospectral pair is given at the end of the chapter.