Central nervous system (CNS) diseases are currently a major challenge in medicine. One reason is the presence of the blood–brain barrier, which is a significant limitation for currently used medicinal substances that are characterized by a high molecular weight and a short half-life. Despite the application of nanotechnology, there is still the problem of targeting and the occurrence of systemic toxicity. Viral vectors and virus-like particles (VLPs) may provide a promising solution to these challenges. Their small size, biocompatibility, ability to carry medicinal substances, and specific targeting of neural cells make them useful in research when formulating a new generation of biological carriers. Additionally, the possibility of genetic modification has the potential for gene therapy. Among the most promising viral vectors are adeno-associated viruses, adenoviruses, and retroviruses. This is due to their natural tropism to neural cells, as well as the possibility of genetic and surface modification. Moreover, VLPs that are devoid of infectious genetic material in favor of increasing capacity are also leading the way for research on new drug delivery systems. The aim of this study is to review the most recent reports on the use of viral vectors and VLPs in the treatment of selected CNS diseases.