The polygenic nature of neurological and psychiatric syndromes and the significant impact of environmental factors on the underlying developmental, homeostatic, and neuroplastic mechanisms suggest that an efficient therapy for these disorders should be a complex one. Pharmacological interventions with drugs selectively influencing the epigenetic landscape (epidrugs) allow one to hit multiple targets, therefore, assumably addressing a wide spectrum of genetic and environmental mechanisms of central nervous system (CNS) disorders. The aim of this review is to understand what fundamental pathological mechanisms would be optimal to target with epidrugs in the treatment of neurological or psychiatric complications. To date, the use of histone deacetylases and DNA methyltransferase inhibitors (HDACis and DNMTis) in the clinic is focused on the treatment of neoplasms (mainly of a glial origin) and is based on the cytostatic and cytotoxic actions of these compounds. Preclinical data show that besides this activity, inhibitors of histone deacetylases, DNA methyltransferases, bromodomains, and ten-eleven translocation (TET) proteins impact the expression of neuroimmune inflammation mediators (cytokines and pro-apoptotic factors), neurotrophins (brain-derived neurotropic factor (BDNF) and nerve growth factor (NGF)), ion channels, ionotropic receptors, as well as pathoproteins (β-amyloid, tau protein, and α-synuclein). Based on this profile of activities, epidrugs may be favorable as a treatment for neurodegenerative diseases. For the treatment of neurodevelopmental disorders, drug addiction, as well as anxiety disorders, depression, schizophrenia, and epilepsy, contemporary epidrugs still require further development concerning a tuning of pharmacological effects, reduction in toxicity, and development of efficient treatment protocols. A promising strategy to further clarify the potential targets of epidrugs as therapeutic means to cure neurological and psychiatric syndromes is the profiling of the epigenetic mechanisms, which have evolved upon actions of complex physiological lifestyle factors, such as diet and physical exercise, and which are effective in the management of neurodegenerative diseases and dementia.