Semiconductor quantum dots are attractive building blocks for scalable quantum information processing systems. The spin-up and spin-down states of a single electon, trapped inside a quantum dot, form a single quantum bit (qubit) with a long decoherence time. The electron spin qubit can be coupled to excited states using an optical field, which provides an opportunity to quickly manipulate the spin with optical pulses, and to interface between a stationary matter spin qubit and a 'flying' photonic qubit for quantum communication. The quantum dot's interaction with light may be enhanced by placing the quantum dot inside of an optical microcavity. Finally, the entire system is monolithically integrated, and modern semiconductor fabrication technology offers a path towards scalability. This work presents experimental developments towards the utilization of single quantum dot electron spins in quantum information processing. We demonstrate a complete set of all-optical single-qubit operations on a single quantum dot spin: initialization, an arbitrary gate, and measurement. First, initialization into a pure spin state (logical 0) is accomplished on a nanosecond timescale by optical pumping. Next an ultrafast single-qubit gate, consisting of a series of broadband laser pulses, rotates the spin to any arbitrary position on the Bloch sphere within 40 picoseconds. Finally, the spin state is measured by photoluminescence detection. We then combine these operations to perform a 'spin echo' sequence on the quantum dot. The spin echo extends the qubit's coherence (memory) time from a few nanoseconds to a few microseconds, more than 10^5 times longer than the single-qubit gate time. We next investigate a feedback mechanism between the electron spin and nuclear spins within the quantum dot, which leads to dynamical pumping of the quantum dot's nuclear magnetization. Finally, we take the first step towards interfacing a stationary matter quantum bit with a flying photonic qubit by strongly-coupling a quantum dot exciton to a pillar microcavity. An anti-crossing of the cavity and excitonic modes indicates that the exciton and cavity modes are coupled more strongly to each other than to the rest of their environment, while photon statistics prove that we have successfully isolated and coupled a single quantum dot exciton.