The BT56 came after one of the most ambitious and troubled cars in Brabham's history. The BT55 had been conceived around a near-horizontal engine installation to achieve an extremely low centre of gravity, but the design's complexity proved unworkable in race conditions. For 1987, the team abandoned that experiment and returned to a more traditional layout.
The departure of Gordon Murray, Brabham's long-serving designer who had moved to McLaren, made the BT56 the first Brabham not designed by Murray since the Ralph Bellamy-designed BT37 that raced in 1972 and 1973. Murray's absence left Baldwin and Rinland to establish a new design direction with less institutional continuity.
The BT56 was powered by the BMW M12/13 four-cylinder turbocharged engine — a unit that had taken Nelson Piquet to the 1983 World Championship with Brabham. The car ran on Goodyear tyres throughout the season. Despite the reversion to conventional design principles, the BT56 never approached the competitiveness of the Williams, McLaren, Ferrari, or Lotus machinery of that era.
The BT56 was the last Brabham Formula One car to use a turbocharged engine. After 1987, the FIA's turbocharged-engine regulations were phased out, and Brabham returned in 1989 with the naturally aspirated Judd V8-powered BT58 following a year's absence from the grid.
The car was driven primarily by Riccardo Patrese and Andrea de Cesaris, with Stefano Modena making additional appearances. Neither driver could challenge the front-running teams consistently, though both recorded third-place finishes during the season. Patrese's came in Mexico and de Cesaris's at Belgium, giving the team a total of 10 points and eighth place in the Constructors' Championship.
Patrese's campaign illustrated the car's mixed potential: he ran as high as second at the San Marino Grand Prix before an alternator failure ended his race, suggesting the BT56 was capable of more than its final results indicated when circumstances aligned. Overall reliability was poor, however, with the drivers combining for only seven race finishes from 16 starts. De Cesaris, despite a reputation for incidents, suffered the majority of his retirements due to mechanical failures rather than accidents.
The 1987 season marked the close of Bernie Ecclestone's ownership of Brabham. Ecclestone had purchased the team in 1972 from co-founder Ron Tauranac for US$120,000 and sold it at the end of 1988 to Swiss businessman Walter Brun for US$5 million. The BT56 thus represented the final Brabham design conceived and raced under Ecclestone's stewardship, closing a chapter that had included four Constructors' Championships and some of the most innovative car designs in the sport's history. The BMW engine specification used in the BT56 was also the last Formula One application of BMW power until 2000, not counting the Megatron-badged derivatives used by Arrows in 1988.