  This chapter emphasizes new magnetic properties that arise when inversion
symmetry is broken in a superconductor. There are two aspects that will be
covered in detail. The first topic encompasses physics related to
superconducting magnetoelectric effects that arise from broken inversion
symmetry. Broken inversion symmetry allow for Lifshitz invariants in the free
energy which can be viewed as a coupling between the magnetic induction and the
supercurrent. There are similarities between these invariants and the better
known Dzyaloshinskii-Moyira interaction in magnetic systems. These Lifshitz
invariants give rise to anomalous magnetic properties as well as new phases in
the presence of magnetic fields. Here, we will describe the consequences of
these Lifshitz invariants, provide estimates for the relative magnitudes of the
novel effects, and discuss the important role that crystal symmetry plays in
understanding this physics. Finally, we provide a discussion of the fate of
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases in broken inversion
superconductors. In particular, we show how broken inversion symmetry can have
a profound effect on the stability, existence, and properties of FFLO phases.
