On 22 November 1955, the Semipalatinsk test site saw the test of the first domestic two-stage thermonuclear RDS-37 charge. The charge operation was based on the principle of radiation implosion. The kernel of the principle consists in the radiation generated in a primary A-bomb explosion and confined by the radiation-opaque casing propagating throughout the interior casing volume and flowing around the secondary thermonuclear unit. The secondary unit experiences a strong compression under the irradiation, with a resulting nuclear and thermonuclear explosion. The RDS-37 explosion was the strongest of all those ever realized at the Semipalatinsk test site. It produced an indelible impression on the participants in the test. This document-based paper describes the genesis of the ideas underlying the RDS-37 design and reflects the critical moments in its development. The advent of RDS-37 was an outstanding accomplishment of the scientists and engineers of our country.