We present our angle-resolved photoemission spectroscopy (ARPES) studies of the cuprate high-temperature superconductors; these studies elucidate the relation between superconductivity and the pseudogap and highlight low-energy quasiparticle dynamics in the superconducting state. Our experiments suggest that the pseudogap and the superconducting gap represent distinct states that coexist below Tc. Studies of Bi-2212 demonstrate that the near-nodal and near-antinodal regions behave differently as a function of temperature and doping, implying that different orders dominate in different momentum-space regions. However, the ubiquity of sharp quasiparticles all around the Fermi surface in Bi-2212 indicates that superconductivity extends into the momentum-space region dominated by the pseudogap, revealing subtlety in this dichotomy. In Bi-2201, the temperature dependence of antinodal spectra reveals particlehole asymmetry and anomalous spectral broadening, which may constrain the explanation for the pseudogap. Noting that electronboson coupling is an important aspect of cuprate physics, we end the paper with a discussion of the multiple kinks in the nodal dispersion. Understanding these will be useful in establishing which excitations are important for superconductivity. Show Partial Abstract