Per-survivor processing (PSP) provides a general framework for the approximation of maximum likelihood sequence estimation (MLSE) algorithms whenever the presence of unknown quantities prevents the precise use of the classical Viterbi algorithm. This principle stems from the idea that data-aided estimation of unknown parameters may be embedded into the structure of the Viterbi algorithm itself. Among the numerous possible applications, the authors concentrate on (a) adaptive MLSE, (b) simultaneous trellis coded modulation (TCM) decoding and phase synchronization, (c) adaptive reduced state sequence estimation (RSSE). As a matter of fact, PSP is interpretable as a generalization of decision feedback techniques of RSSE to decoding in the presence of unknown parameters. A number of algorithms for the simultaneous estimation of data sequence and unknown channel parameters are presented and compared with "conventional" techniques based on the use of tentative decisions. Results for uncoded modulations over interSymbol interference (ISI) fading channels and joint TCM decoding and carrier synchronization are presented. In all cases, it is found that PSP algorithms are clearly more robust than conventional techniques both in tracking a time-varying channel and acquiring its characteristics without training.>