In this thesis we presented some of advantages and applications of FPGAs and what distinguish them from other technologies like CPLDs and ASICs. We also give a brief idea about the major companies in this field. We also introduced some information about the programming languages used to program FPGAs After that we talked about the aspects of FPGAs and its uses in arithmetic algorithms, with examples on how to implement the basic arithmetic circuits like adders, multipliers, dividers in addition to prime number checkers with the help of the MATLAB software and its tools. In addition to these examples we demonstrated some more advanced examples to examine the practicality of using MATLAB with FPGAs in some fields.