  Interaction of solid state qubits with environmental degrees of freedom
strongly affects the qubit dynamics, and leads to decoherence. In quantum
information processing with solid state qubits, decoherence significantly
limits the performances of such devices. Therefore, it is necessary to fully
understand the mechanisms that lead to decoherence. In this review we discuss
how decoherence affects two of the most successful realizations of solid state
qubits, namely, spin-qubits and superconducting qubits. In the former, the
qubit is encoded in the spin 1/2 of the electron, and it is implemented by
confining the electron spin in a semiconductor quantum dot. Superconducting
devices show quantum behavior at low temperatures, and the qubit is encoded in
the two lowest energy levels of a superconducting circuit. The electron spin in
a quantum dot has two main decoherence channels, a (Markovian) phonon-assisted
relaxation channel, due to the presence of a spin-orbit interaction, and a
(non-Markovian) spin bath constituted by the spins of the nuclei in the quantum
dot that interact with the electron spin via the hyperfine interaction. In a
superconducting qubit, decoherence takes place as a result of fluctuations in
the control parameters, such as bias currents, applied flux, and bias voltages,
and via losses in the dissipative circuit elements.
