The spontaneous, uniform orientation of atomic or molecular magnetic moments to generate what is collo- quially called a magnet (more correctly, a ferromagnet) has been explored for more than 2,500 years. Barely a century ago, it was discovered that spontaneous order- ing of electric dipole moments can occur as well 1 . This phenomenon was named ferroelectricity because of the analogies to ferromagnetism, such as the hysteretic switching between two stable states in an external field. Although the technological merits of ferromagnetism and ferroelectricity are quite different, attempts were made to combine them in the same phase of a mat- erial to create a so-called multiferroic material (BOX 1). Multiferroic materials are interesting mainly for two reasons. On the one hand, they make it possible to exploit the functionalities of both orders; for example, a magnetic bit may be complemented by an electric bit to establish a four-state memory element. On the other hand, a coupling between the ferromagnetic and the ferroelectric states might induce novel functionalities not present in either state alone. The control of the magnetic properties by electric fields instead of magnetic fields is an example of the advantages that multiferroic materials can offer. In the reading and writing of a magnetic bit, if a voltage pulse can be used instead of a magnetic-field- generating electric current, the waste heat and relatively long build-up time associated with electric currents are avoided. Multiferroics may thus lead to faster, smaller, more energy-efficient data-storage technologies. The field of multiferroics covers aspects ranging from technological applications to abstract problems of fundamental research. In addition, the study of multi- ferroics increasingly influences neighbouring research areas, such as complex magnetism and ferroelectric- ity, oxide heterostructures and interfaces, and also seemingly remote subjects such as cosmology. In this Review, we give an overview of the twists and turns in the development of the diverse field of multiferroics, and we discuss the trends and challenges that will define its future. Readers looking for a more comprehensive or more technical coverage are referred to more extensive general reviews 2,3 , or to reviews on particular aspects that are highlighted in further sections. We begin with a brief survey of the early days of multi- ferroics. The realization that in some important classes of materials, magnetic and electric long-range order compete with each other 4 may be regarded as the mile- stone separating historical from contemporary research in this field. We continue with an overview of mecha- nisms permitting the coexistence of magnetic and ferro- electric order, and evaluate their potential for inducing pronounced magnetoelectric coupling effects (BOX 1). We then scrutinize heterostructures and, in particu- lar, interfaces that introduce additional functionalities, bringing multiferroics closer to device applications. Domains and domain walls are also discussed: any type of coupling between magnetic and electric long-range order in a multiferroic material has its roots in the cou- pling between the magnetic and electric domains. We then have a closer look at the non-equilibrium dynam- ics of multiferroic materials, because, considering that the focus in multiferroics is on the manipulation of the magnetic order by electric fields, it is very important to understand the processes and timescales governing the magnetoelectric coupling. Important progress in the understanding of the coupling of magnetic and electric Department of Materials, ETH Zürich, Vladimir-Prelog-Weg 4, 8093 Zürich, Switzerland. All authors contributed equally to this work. Correspondence to M.F.  manfred.fiebig@mat.ethz.ch Article number: 16046 doi:10.1038/natrevmats.2016.46 Published online 5 Jul 2016 The evolution of multiferroics Manfred Fiebig, Thomas Lottermoser, Dennis Meier and Morgan Trassin Abstract | Materials with a coexistence of magnetic and ferroelectric order — multiferroics — provide an efficient route for the control of magnetism by electric fields. The study of multiferroics dates back to the 1950s, but in recent years, key discoveries in theory, synthesis and characterization techniques have led to a new surge of interest in these materials. Different mechanisms, such as lone-pair, geometric, charge-ordering and spin-driven effects, can support multiferroicity. The general focus of the field is now shifting into neighbouring research areas, as we discuss in this Review. Multiferroic thin-film heterostructures, device architectures, and domain and interface effects are explored. The violation of spatial and inversion symmetry in multiferroic materials is a key feature because it determines their properties. Other aspects, such as the non-equilibrium dynamics of multiferroics, are underrated and should be included in the topics that will define the future of the field. NATURE REVIEWS | MATERIALS VOLUME 1 | AUGUST 2016 | 1 REVIEWS ©2016MacmillanPublishersLimited,partofSpringerNature.Allrightsreserved.