This is a report on joint work with Ragnar Buchweitz. We investigate homological properties that are invariant under linkage. These properties are finer than Cohen-Macaulayness or perfection, and include the depth and local cohomology of normal modules and twisted conormal modules, cohomology modules of the cotangent complex, and properties of the Yoneda Ext-algebra. These results can be used to distinguish linkage classes, and they have applications in deformation theory and the study of secant and join varieties, for instance.