We discuss first-principles simulations of angle-resolved photoemission (ARPES) intensity in Bi2212 where the photoexcitation process is modeled realistically by taking into account the full crystal wavefunctions of the initial and final states in the presence of the surface. Some recent results aimed at understanding the effects of the energy and polarization dependencies of the ARPES matrix element are presented. The nature of the Fermi surface (FS) maps obtained via ARPES by holding the initial state energy fixed at the Fermi energy (EF) is clarified. The theoretically predicted FS map at 21eV photon energy displays a remarkable level of agreement with the corresponding ARPES spectrum taken over a large area of the (kx,ky) plane. Our analysis shows how the ARPES matrix element can help disentangle closely spaced energy levels and FS sheets and highlight different aspects of the electronic spectrum in complex materials under various experimental conditions.