Existing maximum-likelihood sequence estimation (MLSE) schemes for channels with memory, resulting in intersymbol interference (ISI), have typically been implemented using the Viterbi algorithm (VA). For memoryless modulation schemes the resulting search complexity is O(ML), where M is the alphabet size and L is the length of the ISI span in channel signaling intervals. This complexity renders the VA impractical for large M and/or L. In this paper we describe the structure and properties of a novel reduced-complexity iterative MLSE scheme based upon the expectation-maximization (EM) algorithm. This reduced-complexity iterative MLSE scheme is shown to have complexity O(LM) at each iteration. The approach provides an attractive alternative to the VA for large signaling alphabets and/or ISI span.