Abstract High-throughput sequencing (HTS) technologies revolutionized the field of molecular biology by enabling large scale whole genome sequencing as well as a broad range of experiments for studying the cell's inner workings directly on DNA or RNA level. Given the dramatically increased rate of data generation, new bioinformatics approaches have been developed to cope with the large amount of sequencing reads obtained in these experiments. In this chapter, we first introduce HTS technologies and their usage in molecular biology and discuss the problem of mapping sequencing reads to their genomic origin. We then in detail describe two approaches that offer very fast heuristics to solve the mapping problem in a feasible runtime. In particular, we describe the BLAT algorithm, and we give an introduction to the Burrows-Wheeler Transform and the mapping algorithms based on this transformation.