In this dissertation, we present two kinds of techniques for incremental sequence comparison whose objective is to save the time for comparing sequences that change over time. The first technique is used when the input sequences are changed incrementally and/or decrementally. More specifically, we may append characters to the head of one sequence and/or remove characters from that of the other sequence. Our goal is to obtain the comparison result of updated sequences by utilizing the outdated comparison result. Some applications are introduced to show how to apply this incremental technique for efficiency gains. The second technique is used when two instances (two pairs of sequences) share high similarities with each other. This technique consists of two stages: (1) partitioning the sequences into smaller segments and performing pairwise segment comparison; and (2) using these comparison results to construct the solution of the original sequence comparison. In the first stage, one instance takes advantage of those common segment comparison results of the other instance. In the second stage, the segment comparison results are combined to produce the solution of each instance. We introduce how to apply this technique for incrementally computing both global and local alignments.