This chapter examines several existing concepts of signed line graphs, with particular attention given to spectral signed line graphs. This concept preserves several properties of ordinary line graphs; for instance, the spectrum of the adjacency matrix remains bounded below by −2. Signed graphs that satisfy this bound but are not signed line graphs are also considered. The chapter explores constructions, examples and spectral properties of signed line graphs in detail. In particular, it is shown that the signed line graph of a signed graph is free of multiple edges if and only if the original signed graph contains no parallel edges of the same sign between the same pair of vertices. Consequently, the signed line graph of a signed graph that admits exactly two parallel edges of opposite signs, creating a negative digon, has no multiple edges. These graphs are referred to as simply signed graphs, and their line graphs are examined thoroughly. Specifically, the spectra of signed doubled graphs, that are simply signed graphs in which each edge forms a negative digon, are computed and analysed.