In this chapter we discuss how the transmitted symbols are detected optimally from a noisy received signal (observation). Based on these results, optimal receiver structures are later developed for the modulation methods presented earlier. The same theoretical framework is the basis for optimal solutions for the following problems: 1. Symbol detection from a received noisy continuous-time signal, or from the corresponding discrete-time sample sequence. We consider first the simplified case of detecting an isolated symbol in case of an AWGN channel model. Then symbol sequence detection in case of an ISI channel is considered. 2. Decoding of error correction codes. 3. Parameter estimation, like estimating the signal amplitude, carrier phase, symbol timing, and other synchronization parameters of the receiver. The Viterbi algorithm is a commonly used efficient implementation algorithm for the optimal sequence detection principle.