Complex brain disorders, including Alzheimer's dementia, sleep disorders, and epilepsy, are chronic conditions that have high prevalence individually and in combination, increasing mortality risk, and contributing to the socioeconomic burden of patients, their families and, their communities at large. Although some literature reviews have been conducted mentioning the available methods and tools used for supporting the diagnosis of complex brain disorders and processing different files, there are still limitations. Specifically, these research works have focused primarily on one single brain disorder, i.e., sleep disorders or dementia or epilepsy. Additionally, existing research initiatives mentioning some tools, focus mainly on one single type of data, i.e., electroencephalography (EEG) signals or actigraphies or Magnetic Resonance Imaging, and so on. To tackle the aforementioned limitations, this is the first study conducting a comprehensive literature review of the available methods used for supporting the diagnosis of multiple complex brain disorders, i.e., Alzheimer's dementia, sleep disorders, epilepsy. Also, to the best of our knowledge, we present the first study conducting a comprehensive literature review of all the available tools, which can be exploited for processing multiple types of data, including EEG, actigraphies, and MRIs, and receiving valuable forms of information which can be used for differentiating people in a healthy control group and patients suffering from complex brain disorders. Additionally, the present study highlights both the benefits and limitations of the existing available tools.