The field of computer algebra can be divided into several mutually related subfields. Some of these are more relevant to combinatorialists than others, but we believe that there are some which should be known better. Therefore, for this overview talk, we have decided not only to discuss the most natural topics forming the subfield sometimes called symbolic combinatorics (featuring algorithms for recurrences and differential equations) but also discuss some of the techniques belonging to two other subfields that may be less known: exact arithmetic (with fast multiplication and working with homomorphic images) and Groebner basis (with techniques for reasoning about polynomial ideals). These topics are at the heart of computer algebra, and we believe that it will be handy for a computationally oriented combinatorialist to know about them.