The field of genomics provides many challenges to computer scientists and mathematicians. The area of computational genomics has been expanding recently, and the timely application of computer science in this field is proving to be an essential component of the large international effort in genomics. In this thesis we address key issues in the different stages of genome research: planning of a genome sequencing project, obtaining and assembling sequence information, and ultimately study, cross-species comparison, and annotation of finished genomic sequence. We present applications of computational techniques to the above areas: (1) In relation to the early stages of a genome project, we address physical mapping, and we present results on the theoretical problem of finding minimum superstrings of hypergraphs, a combinatorial problem motivated by physical mapping. We also present a statistical and simulation study of "walking with clone-end sequences", an important method for sequencing a large genome.