The review is devoted to analysis of recent advances, problems, and practical applications of enzymes in the framework of chemical enzymology and enzyme engineering. The achievements in the fundamental understanding of the molecular mechanisms of the catalytic cycle of enzymatic reactions are considered using quantum/molecular mechanics methods with supercomputer technologies and bioinformatics methods. The construction of protein biocatalysts with new properties is a fundamentally significant methodology of the bioengineering approach to solving practical problems, which is demonstrated by a number of examples. The increasing role of biocatalysis in medicine and biomedical research is illustrated by solving the problems of antibiotic synthesis and overcoming bacterial resistance to them, studying the mechanisms of neurodegenerative diseases and developing drugs to treat Alzheimer's disease, and investigation of biocatalytic processes of DNA repair and the role of mechanisms of functioning of heme peroxidases in the human body. The use of enzymes that destroy various endogenous and exogenous toxicants has been greatly developed in recent decades. The problems of using enzymes in therapy and drug delivery are analyzed. The fundamental role of enzymes in modern analysis and diagnosis is noted. The review considers a new trend in the development of bioanalytical methods using aptamers, multianalytical biochips, surface-enhanced Raman scattering systems, and bioelectroanalysis.<br> The bibliography includes 460 references.