<p>Cage graphs are vertex-regular graphs with a given girth, and they find several chemical and biological applications including the representations of isomerization reaction pathways and other chemical and biological networks. A <i>(d</i>,<i> g</i>)- cage contains all vertices with the same degree <i>d</i> and has a girth <i>g</i>. In chemical applications trivalent-cages play especially important roles, as exemplified by the applications to dynamic stereochemistry. Several of the cage graphs exhibit very high order of symmetries, and hence highly degenerate spectra and often integral spectra. The cage graphs have a long and rich history of research-span tracing back to Kárteszi, Sachs and Erdös. We obtain fully expanded spectral polynomials, graph spectra and a number of distance and degree based descriptors, graph energies and entropies of several mathematically and chemically interesting cages. The spectral polynomials of the cages are computed through powerful bit-manipulation algorithms. We have considered both vertex-transitive cages and cages with multiple or single automorphic vertex equivalence classes of vertices. Computations were carried out using high degree of precision to enumerate the coefficients of the spectral polynomials and other properties. The mathematical properties and the coefficients in the polynomials were further dissected and analysed to provide structural interpretations.</p>