The paper reviews the latest angle-resolved photoemission spectroscopy (ARPES) results on cuprate superconductors and their insulating parent and sister compounds. It discusses low-energy excitations, including Fermi surface and remnant Fermi surface states, pseudogap and d-wave-like dispersion, evidence of electronic inhomogeneity and nano-scale phase separation, coherent quasiparticles through the superconducting transition, and many-body effects in the one-particle spectral function. The authors focus on experimental data due to the dynamic nature of the field, providing a snapshot of the current state of ARPES in the study of high-$T_c$ superconductors. The paper covers the scientific issues relevant to investigating the low-energy electronic structure by ARPES, including normal-state electronic structure, interlayer interaction, superconducting gap, coherent superconducting peak, pseudogap, electron self-energy, and collective modes. The review is organized along conceptual lines, discussing each topic in the context of different cuprate superconductors.The paper reviews the latest angle-resolved photoemission spectroscopy (ARPES) results on cuprate superconductors and their insulating parent and sister compounds. It discusses low-energy excitations, including Fermi surface and remnant Fermi surface states, pseudogap and d-wave-like dispersion, evidence of electronic inhomogeneity and nano-scale phase separation, coherent quasiparticles through the superconducting transition, and many-body effects in the one-particle spectral function. The authors focus on experimental data due to the dynamic nature of the field, providing a snapshot of the current state of ARPES in the study of high-$T_c$ superconductors. The paper covers the scientific issues relevant to investigating the low-energy electronic structure by ARPES, including normal-state electronic structure, interlayer interaction, superconducting gap, coherent superconducting peak, pseudogap, electron self-energy, and collective modes. The review is organized along conceptual lines, discussing each topic in the context of different cuprate superconductors.