Schizophrenia is a socially significant mental disorder resulting frequently in severe forms of disability. Diagnosis, choice of treatment tactics, and rehabilitation in clinical psychiatry are mainly based on the assessment of behavioral patterns, socio-demographic data, and other investigations such as clinical observations and neuropsychological testing including examination of patients by the psychiatrist, self-reports, and questionnaires. In many respects, these data are subjective and therefore a large number of works have appeared in recent years devoted to the search for objective characteristics (indices, biomarkers) of the processes going on in the human body and reflected in the behavioral and psychoneurological patterns of patients. Such biomarkers are based on the results of instrumental and laboratory studies (neuroimaging, electro-physiological, biochemical, immunological, genetic, and others) and are successfully being used in neurosciences for understanding the mechanisms of the emergence and development of nervous system pathologies. Presently, with the advent of new effective neuroimaging, laboratory, and other methods of investigation and also with the development of modern methods of data analysis, machine learning, and artificial intelligence, a great number of scientific and clinical studies is being conducted devoted to the search for the markers which have diagnostic and prognostic value and may be used in clinical practice to objectivize the processes of establishing and clarifying the diagnosis, choosing and optimizing treatment and rehabilitation tactics, predicting the course and outcome of the disease. This review presents the analysis of the works which describe the correlates between the diagnosis of schizophrenia, established by health professionals, various manifestations of the psychiatric disorder (its subtype, variant of the course, severity degree, observed symptoms, etc.), and objectively measured characteristics/quantitative indicators (anatomical, functional, immunological, genetic, and others) obtained during instrumental and laboratory examinations of patients. A considerable part of these works has been devoted to correlates/biomarkers of schizophrenia based on the data of structural and functional (at rest and under cognitive load) MRI, EEG, tractography, and immunological data. The found correlates/biomarkers reflect anatomic disorders in the specific brain regions, impairment of functional activity of brain regions and their interconnections, specific microstructure of the brain white matter and the levels of connectivity between the tracts of various structures, alterations of electrical activity in various parts of the brain in different EEG spectral ranges, as well as changes in the innate and adaptive links of immunity. Current methods of data analysis and machine learning to search for schizophrenia biomarkers using the data of diverse modalities and their application during building and interpretation of predictive diagnostic models of schizophrenia have been considered in the present review.