In this article, we investigate the class of multivariate quadratic (MQ) public key systems. These systems are becoming a serious alternative to RSA or ECC based systems. After introducing the main ideas and sketching some relevant systems, we deal with the advantages and disadvantages of these kinds of schemes. Based on our observations, we determine application domains in which MQ-schemes have advantages over RSA or ECC. We concentrate on product activation keys, electronic stamps and fast one-way functions