Infertility is a major health problem worldwide without an effective therapy or cure. It is estimated to affect 8–12% of couples in the reproductive age group, equally affecting both genders. There is no single cause of infertility, and its knowledge is still far from complete, with about 30% of infertile couples having no cause identified (named idiopathic infertility). Among male causes of infertility, asthenozoospermia (i.e., reduced sperm motility) is one of the most observed, being estimated that more than 20% of infertile men have this condition. In recent years, many researchers have focused on possible factors leading to asthenozoospermia, revealing the existence of many cellular and molecular players. So far, more than 4000 genes are thought to be involved in sperm production and as regulators of different aspects of sperm development, maturation, and function, and all can potentially cause male infertility if mutated. In this review, we aim to give a brief overview of the typical sperm flagellum morphology and compile some of the most relevant information regarding the genetic factors involved in male infertility, with a focus on sperm immotility and on genes related to sperm flagellum development, structure, or function.