  We discuss recent advances in developing a mode-coupling theory of the glass
transition (MCT) of two-dimensional systems of active Brownian particles (ABP).
We specifically discuss the case of a single ABP tracer in a glass-forming
passive host suspension; a case that has recently been studied in experiments
on colloidal Janus particles. We employ event-driven Brownian dynamics (ED-BD)
computer simulations to test the ABP-MCT, and find good agreement between the
two for the MSD. The ED-BD simulation results also compare well to experimental
data, although a peculiar non-monotonic mapping of self-propulsion velocities
is required. The ABP-MCT predicts a specific self-propulsion dependence of the
Stokes-Einstein relation between the long-time diffusion coefficient and the
host-system viscosity that matches well the results from simulation. An
application of ABP-MCT within the integration-through transients (ITT)
framework to calculate the density-renormalized effective swim velocity of the
interacting ABP agrees qualitatively with the ED-BD simulation data at
densities close to the glass transition, and quantitatively for the full
density range only after the mapping of packing fractions employed for the
passive system.
