The majority of massive stars are born in close binary systems with orbital periods of a few days. At some point during their core-hydrogen burning phase, both members of these close binaries inevitably overflow their Roche lobes simultaneously and get bound by a common equipotential surface. The characteristics of this `contact phase’ will determine the fate of the binary system: whether the stars will merge on the main sequence or evolve further towards becoming potential gravitational-wave progenitors. Although data is available for several of these massive contact binaries in the Magellanic Clouds and the Milky Way, there has not been a dedicated study of these systems so far. In this talk, I will present the first set of detailed binary models covering a wide range of initial masses (20-80 Msun) and initial periods (0.6-2 days), focusing especially on the properties of the contact phase. We find that our models can approximately reproduce the period-mass ratio trend of the observed binaries although for the higher masses of our grid, our model predictions do not match with what is observed. We also find that those binary models which are in contact over nuclear timescales evolve towards equal masses before ultimately merging on the main sequence. This first study of massive contact binaries has allowed us to gain insights into the physics of massive contact systems and also provide reasonable predictions for the final fate of close massive binary stars.