The importance of solid-state surfaces for many applications, from electronics to heterogenous catalysis, has been known for decades. Less established is the fact that surfaces are also a platform for emergent phenomena that are forbidden by symmetry constraints from existing deep inside the material bulk. The low-symmetry environment of surfaces and interfaces (even in the absence of additional surface reconstructions) can allow for functional, surface-localized properties ranging from a finite surface magnetization for bulk antiferromagnets, surface magnetoelectric effects, spin and anomalous Hall transport effects, topologically protected electronic surface states, surface ferroelectricity, and more. These emergent surface phenomena have the potential to transform current device architectures, in particular for spintronics applications where the electron spin degree of freedom, in addition to its charge, is used to store and transport information. The magnetic, topological and magnetotransport features of surfaces can be used to both detect and manipulate the properties of the underlying material bulk as well as of other, interfaced materials. Moreover, these low-symmetry surface properties can be quite large due to their intrinsic energy scale, which is set by the material crystal field. Thus, exploiting emergent surface properties rather than focusing on bulk features could pave the way to logic, storage and computing technologies with improved energy-efficiency and robustness. Although the theoretical concept of low-symmetry surface properties has been been known (but under-recognized) for some time, first-principles calculations that quantitatively predict and characterize these emergent surface properties in realistic materials are still in their infancy. The proposed project aims to advance the fundamental understanding of surface phenomena such as surface magnetization, topological and non-topological Anomalous Hall and magnetoelectric effects, and surface ferroelectricity, that arise due to intrinsic symmetry-lowering at surfaces and interfaces. This will be accomplished by using state-of-the-art density functional theory (DFT), supplemented with tight-binding calculations and Monte Carlo simulations. We will focus on several complementary goals, including understanding the underlying microscopic mechanisms that influence the magnitude of these surface properties; determining cross-coupling capabilities for coexisting surface features (for example, surface polarization and magnetization); and predicting new materials where these surface properties are optimized. The broad range of properties to be investigated in this proposal necessitates a variety of methods with differing levels of computational overhead. To model the magnetic materials of interest, the DFT+U method will be used. Constrained, noncollinear magnetic DFT will also be leveraged to explore energy landscapes for surface and bulk magnetic order in slab geometries. To explore surface magnetoelectric and other electric field-induced properties, we will simulate applied electric fields within DFT at various levels of theory. Tight-binding models built from bulk DFT calculations using the Wannier90 code will enable computationally tractable evaluation of topological invariants and topological surface states. Finally, we will endeavor to connect our theoretical predictions to surface-sensitive experimental measurements, for example by calculating material-specific dielectric responses within DFT, and evaluating temperature-dependent magnetic properties using Monte Carlo simulations.