Shannon's classical channel capacity is not the only notion of capacity to have been studied by information theorists. Others include, inter alia, the zero-error capacity, the zero-undetected-error capacity, and the mismatch capacity. In this talk I shall survey some of these capacities with special emphasis on their behavior in the presence of a feedback link from the channel output to the encoder. The relationship, first observed by Csiszár and Narayan, between the mismatch capacity and the zero-undetected-error capacity, will allow us to use the results on the latter's feedback behavior to study the former's. With this approach we will show that feedback can increase the mismatch capacity; we will derive conditions that guarantee that the feedback mismatch capacity equals Shannon's capacity; and we will derive new achievable rates for the cases where these conditions are not satisfied.