In a 2d conformal field theory (CFT) the central charge, defined from the Virasoro algebra, provides a measure of the number of CFT degrees of freedom. Crucially, the c-theorem provides a powerful universal and non-perturbative constraint on the central charge: it must decrease under renormalization group flows. The central charge appears in many other places too, such as stress-tensor two-point functions, thermal entropy, entanglement entropy, and so on. However, what happens with a two-dimensional conformal defect in a higher-dimensional CFT, or at the boundary of a 3d CFT? Generically in these cases no Virasoro algebra is present. Can we still define a central charge? If so, in what quantities does it appear? Can we prove a c-theorem? These questions may be crucial for graphene with a boundary, surface operators in gauge theory CFTs, and many other systems. In this talk I will summarize the state of the art in this area, including results for example systems and open questions.