  Multiferroics are those materials with more than one ferroic order, and
magnetoelectricity refers to the mutual coupling between magnetism and
electricity. The discipline of multiferroicity has never been so highly active
as that in the first decade of the twenty-first century, and it has become one
of the hottest disciplines of condensed matter physics and materials science. A
series of milestones and steady progress in the past decade have enabled our
understanding of multiferroic physics substantially comprehensive and profound,
which is further pushing forward the research frontier of this exciting area.
The availability of more multiferroic materials and improved magnetoelectric
performance are approaching to make the applications within reach. While
seminal review articles covering the major progress before 2010 are available,
an updated review addressing the new achievements since that time becomes
imperative. In this review, following a concise outline of the basic knowledge
of multiferroicity and magnetoelectricity, we summarize the important research
activities on multiferroics, especially magnetoelectricity and related physics
in the last six years. We consider not only single-phase multiferroics but also
multiferroic heterostructures. We address the physical mechanisms regarding
magnetoelectric coupling so that the backbone of this divergent discipline can
be highlighted. A series of issues on lattice symmetry, magnetic ordering,
ferroelectricity generation, electromagnon excitations, multiferroic domain
structure and domain wall dynamics, and interfacial coupling in multiferroic
heterostructures, will be revisited in an updated framework of physics. In
addition, several emergent phenomena and related physics, including magnetic
skyrmions and generic topological structures associated with magnetoelectricity
will be discussed.
