For varifolds with bounded first variation, the monotonicity formula is the starting point for much of the classical regularity theory: it provides density estimates, compactness, and ultimately Allard's regularity theorem. For general anisotropic surface energies, however, no analogous monotonicity formula is available. I will describe an alternative approach to anisotropic varifolds based on the Michael–Simon inequality. We prove an anisotropic Michael–Simon inequality in arbitrary dimension and codimension for a broad class of surface energies, including every convex hypersurface anisotropy. The proof is based on a projection method for anisotropic stress measures that converts the geometric problem into a non-concentration problem for matrix-valued measures with controlled divergence. I will then explain how this inequality can replace monotonicity in the regularity theory. In particular, it yields density and compactness estimates and, combined with an ε-regularity argument, an anisotropic version of Allard's theorem in arbitrary codimension for a natural class of anisotropies. This is based on joint work with Benjy Firester and Antonio De Rosa.