The rapid growth of biotechnologies, especially in large sequencing projects, has lead to an explosion of genomic data. For molecular biologists, this mass of data is potentially a rich source of knowledge with appropriated n-silico processes. From a computational point of view, the data to manipulate are basically text sequences (protein or DNA), and the main task consist in computing similarities. This falls into the string processing computation family which has been studied for a long time, and where numerous parallel architectures have been proposed. FPGA are well suited for implementing these regular structures and dedicated reconfigurable accelerators have naturally been designed to speed-up the main bioinformatic programs. Today, commercial products, based on previous academic researches, exibit impressive performance compared to parallel machines. In this chapter, we have first introduced some important genomic applications to highlight the computer power need. Then, we focussed on the algorithmic part and their associated hardware implementation: (1) the historical programing dynamic algorithm has been detailed together with its systolic structure; (2) more recent works on seed-based heuristics to rapidely search genomic banks have been explained; (3) HMMs and language models to perform more complex computations have been presented. Finally, we concluded with some realisations of FCCM accelerators dedicated to genomic computations.