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The 2018 Gordon Research Conference on Multiferroic and Magnetoelectric Materials is the third in a series of biennial meetings that present the latest developments and advances in the investigation, design, and applications of multifunctional materials with coexisting magnetic and ferroelectric order. Research on multiferroics was initially dominated by the search for new compounds and mechanisms combining magnetic and ferroelectric order as well as fostering large magnetoelectric coupling effects between them. In the last few years, in addition, concepts from multiferroics have begun to infiltrate research areas in which magnetoelectric coupling is no longer the driving interest. For example, in the field of ferroelectrics, a rich variety of new mechanisms have been identified that allow ferroelectricity to coexist with magnetism. In optics, the violation of spatial and inversion symmetry in multiferroic materials promotes a variety of unusual effects, such as nonreciprocal directional dichroism. New and improved experimental detection techniques and theoretical methods have been developed to investigate multiferroics and their magnetoelectric correlations. The functional and mobile interfaces provided by multiferroic domain walls is taking oxide electronics in a new direction. Multiferroics have been shown to host exotic topological states such as skyrmions, domain vortices or even unconventional superconductivity. And finally, the new area of dynamical processes in multiferroics is providing a rich system for studying spin, electronic and lattice dynamics and the coupling between them. The 2018 GRC will highlight these emerging topics and developments, as well as review progress in the core applications area of electric-field control of magnetism. For this purpose, the meeting will bring together scholars from diverse scientific disciplines to promote discussion, kick-start collaborations across the boundaries of individual disciplines, and convey the enormous potential of multiferroics research to a new generation of young researchers and students.