Block-interchanges are a new kind of genome rearrangements that affect the gene order in a chromosome by swapping two nonintersecting blocks of genes of any length. More recently, the study of such rearrangements is becoming increasingly important because of its applications in molecular evolution. Usually, this kind of study requires to solve a combinatorial problem, called the block-interchange distance problem, which is to find a minimum number of block-interchanges between two given gene orders of linear/circular chromosomes to transform one gene order into another. In this chapter, we shall introduce the basics of block-interchange rearrangements and permutation groups in algebra that are useful in analyses of genome rearrangements. In addition, we shall present a simple algorithm on the basis of permutation groups to efficiently solve the block-interchange distance problem, as well as ROBIN, a web server for the online analyses of block-interchange rearrangements.