This chapter discusses mathematical and computational methods that enhance the modeling, optimization, and analysis of high-resolution DNA melting assays. In conjunction with recent improvements in reagents and hardware, these algorithms have enabled new closed-tube techniques for genotyping, mutation scanning, confirming or ruling out genotypic identity among living related organ donors, and quantifying constituents in samples containing different DNA sequences. These methods are rapid, involving only 1 to 10 min of automatic fluorescence acquisition after a polymerase chain reaction. They are economical because inexpensive fluorescent dyes are used rather than fluorescently labeled probes. They are contamination-free and nondestructive. Specific topics include methods for extracting accurate melting curve information from raw signal, for clustering and classifying the results, for predicting complete melting curves and not just melting temperatures, and for modeling and analyzing the behavior of mixtures of multiple duplexes.