Cognitive impairment by neurotoxic substances, administered alone or in a multidrug regimen, affects a large number of patients treated for noncentral nervous system cancer during and after chemotherapy with variable onset, severity and duration, but sustainably affecting the patients’ individual health-related quality of life. Depending on the mechanism of action, the ability to cross the blood–brain barrier into the central nervous system and the cumulative total dose of the cytotoxic drugs results in functional and structural brain changes. This neurotoxicity leads to negative effects on neural precursor cells (neurogenesis), microglia (neuroinflammation), neurons (cortical dysfunction with altered brain networks), and astro-/oligodendroglia (white matter tract demyelination) and therefore on patients’ cognitive performance. Memory and executive functions, attention/concentration, and processing speed are the cognitive domains commonly impaired by chemotherapy. Importantly, numerous simultaneously occurring risk factors may also have distinct restrictions on cognitive function. For this reason, the term cancer-related cognitive impairment (CRCI), implicating neurotoxicity in cancer patients with simultaneous consideration of other causes on cognitive performance, should be used. The aim of this review is to provide an update of the most recent clinical and pathophysiological findings, self-reported and neuropsychological testing methods, and the current management strategies of CRCI.