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.
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