We give a survey of some recent work about type-based complexity analysis methodologies for functional programs and processes. We will focus, in particular, on techniques drawn from linear logic. The latter indeed enables, through exponential modalities, a fine control of the copying phenomenon, itself responsible for the high complexity of cut-elimination. Our journey starts from simple but intentionally very poor fragments, like light and soft linear logic, and progressively moves towards more expressive type-systems, ending up in linear dependent types, which are well-known to be relatively complete. If time permits, we will report on our ongoing work about applying linear dependent types to pi-calculus processes