Achieving control over the electron spin in quantum dots (artificial atoms) or real atoms promises access to new technologies in conventional and quantum information processing. Here we review our proposal for quantum computing with the spins of electrons confined to quantum dots. We discuss the basic requirements for implementing spin qubits, and describe a complete set of quantum gates for single- and two-qubit operations. We show how a quantum dot attached to leads can be used for spin filtering and spin read-out, and as a spin-memory device. Finally, we focus on the experimental characterization of the quantum dot systems, and discuss transport properties of a double-dot and show how Kondo correlations can be used to measure the Heisenberg exchange interaction between the spins of two dots.