  A qubit subjected to pure dephasing due to classical Gaussian noise can be
turned into a spectrometer of this noise by utilizing its readout under
properly chosen dynamical decoupling (DD) sequences to reconstruct the power
spectral density of the noise. We review the theory behind this DD-based noise
spectroscopy technique, paying special attention to issues that arise when the
environmental noise is non-Gaussian and/or it has truly quantum properties.
While we focus on the theoretical basis of the method, we connect the discussed
concepts with specific experiments and provide an overview of environmental
noise models relevant for solid-state based qubits, including quantum-dot based
spin qubits, superconducting qubits, and NV centers in diamond.
