It was the first of the Volvo BXXR series, replacing the higher output configurations of the B12B.

The B13R is easy recognisable as being the only modern Volvo coach chassis with air intakes on the right-hand side.

After launch in 2009 it soon became the default choice of chassis for Volvo's 9700 and 9900 coaches, as only the 340 hp configuration of the B12B was compatible with the Euro V requirements.

The lowest configuration of the 9700; the 9700S, was not compatible with the B13R, as the engine was so tall that it would conflict with the internal floor.

Volvo later reintroduced the B13R chassis, on 30 June 2022, featuring Euro VI-compliant D13K engines.