  Multiferroics, defined for those multifunctional materials in which two or
more kinds of fundamental ferroicities coexist, have become one of the hottest
topics of condensed matter physics and materials science in recent years. The
coexistence of several order parameters in multiferroics brings out novel
physical phenomena and offers possibilities for new device functions. The
revival of research activities on multiferroics is evidenced by some novel
discoveries and concepts, both experimentally and theoretically. In this review
article, we outline some of the progressive milestones in this stimulating
field, specially for those single phase multiferroics where magnetism and
ferroelectricity coexist. Firstly, we will highlight the physical concepts of
multiferroicity and the current challenges to integrate the magnetism and
ferroelectricity into a single-phase system. Subsequently, we will summarize
various strategies used to combine the two types of orders. Special attentions
to three novel mechanisms for multiferroicity generation: (1) the
ferroelectricity induced by the spin orders such as spiral and E-phase
antiferromagnetic spin orders, which break the spatial inversion symmetry, (2)
the ferroelectricity originating from the charge ordered states, and (3) the
ferrotoroidic system, will be paid. Then, we will address the elementary
excitations such as electromagnons, and application potentials of
multiferroics. Finally, open questions and opportunities will be prospected.
