Neurological diseases are responsible for approximately 6.8 million deaths every year. They affect up to 1 billion people worldwide and cause significant disability and reduced quality of life. In most neurological disorders, the diagnosis can be challenging; it frequently requires long-term investigation. Thus, the discovery of better diagnostic methods to help in the accurate and fast diagnosis of neurological disorders is crucial. Circulating nucleic acids (CNAs) are defined as any type of DNA or RNA that is present in body biofluids. They can be found within extracellular vesicles or as cell-free DNA and RNA. Currently, CNAs are being explored as potential biomarkers for diseases because they can be obtained using non-invasive methods and may reflect unique characteristics of the biological processes involved in several diseases. CNAs can be especially useful as biomarkers for conditions that involve organs or structures that are difficult to assess, such as the central nervous system. This review presents a critical assessment of the most current literature about the use of plasma and serum CNAs as biomarkers for several aspects of neurological disorders: defining a diagnosis, establishing a prognosis, and monitoring the disease progression and response to therapy. We explored the biological origin, types, and general mechanisms involved in the generation of CNAs in physiological and pathological processes, with specific attention to neurological disorders. In addition, we present some of the future applications of CNAs as non-invasive biomarkers for these diseases.