Pilocytic and pilomyxoid astrocytomas are some of the most common gliomas in children and young adults. These gliomas are indolent neoplasms with long overall survival probability. The genetic characteristics of these neoplasms are well known, and our deepened understanding of their associated molecular alterations has led to the development of novel treatment strategies and approaches. Currently, we can account for some of the unusual behavior, such as oncogene-induced senescence, associated spontaneous regression, anaplastic transformation, and cerebrospinal dissemination, of these gliomas. Nevertheless, enigmatic issues continue to surround these chronic tumors. Here, we review the classical and uncommon clinical pathological and genetic features of these indolent gliomas.