  We briefly review the theoretical formulations and applications of the
Aharonov--Bohm effect and the Aharonov--Casher effect with emphasis on
mesoscopic physics. Topics relating to the Aharonov--Bohm effect include:
locality, periodicity, non-integrable phase factors, Abelian gauge theory,
interference, the spectrum and persistent current of electrons on a ring
pierced by a magnetic field, Onsager reciprocity relations, and Aharonov--Bohm
interferometer. Topics relating to the Aharonov--Casher effect include: a
magnetic dipole in an electric field, locality, periodicity, non-Abelian gauge
invariance, SU(2) non-integrable phase factors, spin-orbit coupling, Pauli
equation, Rashba Hamiltonian, Aharonov--Casher interferometer, conductance and
polarization in two-channel systems due to the Aharonov--Casher effect.
