Six single-seat Saab AJ 37 Viggen prototypes and one two-seat Sk 37 Viggen prototype were ordered in 1965, at about the same time a mockup of the aircraft was displayed to the media. The first single-seat prototype was rolled out on November 24, 1966 and performed its initial flight on February 8, 1967, with Erik Dahlstrom, SAAB's chief test pilot, at the controls.

The SAAB 37 Viggen aircraft had a novel and advanced aerodynamic configuration to meet the short take-off/landing and other performance requirements: a fixed foreplane with flaps was mounted ahead of and slightly above the delta main wing.

The aircraft's main wings are low-mounted, delta-shaped, extending from the body midsection to the exhaust. Small, clipped delta wings are forward of the main wings and high-mounted on the body. There is one turbofan engine in the body. There are semicircular air intakes just forward and below the secondary wings. There is a large, single exhaust. The fuselage is short and wide with a pointed, solid nose. There is a bubble canopy and a small belly fin. There are no tail flats. There is a large, unequally tapered fin with a small, clipped tip.

- Saab 37 prototype.

- AJ 37 attack variant, with secondary air combat capability.

- SK 37 two-seat operational conversion trainer.

- SK 37E countermeasures upgrade SK 37.

- SH 37 maritime reconnaissance and strike variant.

- SF 37 dedicated reconnaissance variant.

- JA 37 interceptor variant, based on an improved airframe.

- AJS 37 upgraded AJ 37.

- AJSF 37 upgraded SF 37.

- AJSH 37 upgraded SH 37.

Only two Saab SK 37E Viggens are operational at the Swedish Air Force for various evaluation tasks.