The past century has seen the ongoing development of amplifiers for different electrophysiological signals to study the work of the heart. Since the vacuum tube era, engineers and designers of bioamplifiers for recording electrophysiological signals have been trying to achieve similar objectives: increasing the input impedance and common-mode rejection ratio, as well as reducing power consumption and the size of the bioamplifier. This review traces the evolution of bioamplifiers, starting from circuits on vacuum tubes and discrete transistors through circuits on operational and instrumental amplifiers, and to combined analog-digital solutions on analog front-end integrated circuits. Examples of circuits and their technical features are provided for each stage of the bioamplifier development. Special emphasis is placed on the review of modern analog front-end solutions for biopotential registration, including their generalized structural diagram and table of comparative characteristics. A detailed review of analog front-end circuit integration in various practical applications is provided, with examples of the latest achievements in the field of electrocardiogram, electroencephalogram, and electromyogram registration. The review concludes with key points and insights for the future development of the analog front-end concept applied to bioelectric signal registration.