Colloidal quantum dots (QDs) are nanoscale semiconductor crystals with surface ligands that enable their dispersion in solvents. Quantum confinement effects facilitate wave function engineering to sculpt the spatial distribution of charge and spin states and thus the energy and dynamics of QD optical transitions. Colloidal QDs can be integrated in devices using solution-based assembly methods to position single QDs and to create ordered QD arrays. Here, we describe the synthesis, assembly, and photophysical properties of colloidal QDs that have captured scientific imagination and have been harnessed in optical applications. We focus especially on the current understanding of their quantum coherent effects and opportunities to exploit QDs as platforms for quantum information science. Freedom in QD design to isolate and control the quantum mechanical properties of charge, spin, and light presents various approaches to create systems with robust, addressable quantum states. We consider the attributes of QDs for optically addressable qubits in emerging quantum computation, sensing, simulation, and communication technologies, e.g., as robust sources of indistinguishable, single photons that can be integrated into photonic structures to amplify, direct, and tune their emission or as hosts for isolated, coherent spin states that can be coupled to light or to other spins in QD arrays.