Genetic Algorithms are an algorithmic paradigm which mimics biological processes that occur in the theory of evolution. Genetic Algorithms have a very wide range of applicability and they are a powerful alternative to conventional search algorithms. The basic principles and the mechanics of Genetic Algorithms will be briefly reviewed and illustrated with a particular application in finding exact solutions to big polynomial systems of equations (corresponding to zero-dimensional ideals) that are not easily solvable (to the best of our knowledge) with any other general-purpose method.