A rich zoo of peculiar objects forms when stars with extended, loosely-bound, convective envelopes undergo gravitational interaction with a binary companion. We investigate the poorly understood evolutionary channels of a family of chemically peculiar stars known as barium (Ba) stars. These main-sequence or giant stars were formed when a former AGB companion, which is now a dim white dwarf, polluted them with heavy elements. A long-standing problem, however, is that their observed properties are not predicted by models, so their formation and evolution are not well understood. I will present results of our long-term radial velocity monitoring programme and a new HR diagram of Ba and related stars. By analysing their period, eccentricity and mass distributions at different evolutionary stages, we aim to investigate the formation and evolution of these systems. By comparing observations with our state-of-the-art BINSTAR  evolutionary models, our ultimate goal is to come to a prescription of the initial conditions and interaction processes required for a binary system to evolve into a Ba giant. This work will give us insight into the effect of binarity along the RGB and the AGB phases.