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The use of coded modulations such as continuous phase modulation (CPM) can improve the power and bandwidth efficiency of digital communication links. The price paid for these gains is in increased receiver complexity. The power efficiency attainable with the highly redundant signal sets employed by coded modulations becomes limited by the ability of the receiver to achieve accurate carrier phase synchronisation. Power efficiency is assessed in terms of the bit error rate performance in white Gaussian noise. A new CPM detector called the partially coherent Viterbi algorithm (PCVA) is introduced which tries to preserve the power efficiency in the presence of mild phase perturbations. The detector employs the Viterbi algorithm with a new partially coherent decision metric. Carrier phase estimates are derived dynamically from the detector's own survivor paths. In the presence of phase jitter, the PCVA is superior to a Viterbi decision directed phase locked loop. The PCVA could be applied to the detection of modulation schemes other than CPM. An error analysis of the PCVA in the absence of phase jitter provides a new and more realistic way of assessing the relative merits of various CPM schemes. Unmerged error events have been found to occur when CPM is detected with carrier phase uncertainty. The carrier phase estimator pulls in the residual phase error in such cases. A reduced state Viterbi algorithm has been examined when using the partially coherent decision metric. Receiver complexity reduction is still possible even when the detector is not coherent. A method of acquiring the carrier frequency accurately from the received CPM signal is described. The other main research goal has been the development of a new low signal-to-noise ratio (SNR) error probability analysis for coherently detected CPM. CPM is designed for use on power limited channels, but the existing error probability analysis is only accurate at high SNR. The problem at low SNR is that several error events become significant, not just the one at minimum squared Euclidean distance. The new analysis considers many events and makes statistical allowance for their pairwise interaction. The probability of events intersecting and reclosing each other has not been analysed before. This work applies to maximum likelihood sequence detection on a memoryless channel in general. A new survey of CPM error performance is made and proves the existing minimum distance results to be often optimistic especially at low and intermediate signal-to-noise ratios. The new approximation is closer to the simulated error rates where these are available. The coherent error analysis involves some computation but it is still approximately three orders of magnitude faster than simulation.