With an increasing incidence of malignancies, the number of patients treated with cytostatic chemotherapy is rising continuously. Neurological sequelae of tumor therapy are a growing concern as improved therapy protocols increase the life expectancy of patients. Despite the postmitotic state of neurons, neurotoxic phenomena are amongst the most common side effects of many cytostatic drugs, second only to hematological or gastroenterological toxicities. Chemotherapy-induced neurotoxic phenomena represent a medical problem as they can be dose limiting, thus preventing optimal therapy, and lead to long-lasting limitations in quality of life. There are hardly any validated therapeutic or preventive approaches to neurotoxic side effects of cytostatic drugs. In view of the large number of possible neurotoxic symptoms, knowledge of chemotherapy-induced neurological pathologies in the central and peripheral nervous system is of practical relevance for making a differential diagnosis. In the context of ever more complex treatment protocols and increasing number of cytostatic drugs, we review the neurological side effects of chemotherapeutic drugs in general use in the peripheral and central nervous system and discuss potential therapeutic strategies. In the first part, this review focuses on side effects in the peripheral nervous system of platinum-based antineoplastic drugs (cisplatin, carboplatin, oxaliplatin), vincaalcaloids (vincristine), taxanes (paclitaxel, docetaxel), proteasome inhibitors (bortezomib) and biologicals (brentuximab-vedotin). The second part is dedicated to neurotoxic side effects in the central nervous system induced by anti-metabolites (methotrexate, 5-fluoruracil, cytarabine, fludarabine), alkylating agents (ifosfamide), platinum-based antineoplastic drugs (cisplatin), vincaalcaloids (vincristine), receptor tyrosine kinase inhibitors (imatinib, sorafenib, sunitinib) and biologicals (bevacizumab). In the third part of this review we summarize current data on the illness entity of chemotherapy-induced cognitive impairment, whose etiology continues to be controversial.