  So far, stellar population studies have mainly focused on the evolution of
single and binary stars. Recent observations show that triple and higher order
multiple star systems are common, especially among massive stars. Introducing
three-body dynamical effects can influence the evolution of an individual
stellar system and hence affect the predicted rates of astrophysical sources
that are a product of stellar evolution. We aim to constrain the main
evolutionary pathways of massive hierarchical triple star systems and to
quantify the effect of the third star on the evolution of the system. We model
the massive triple star population by performing simulations of triple star
evolution with the TRES code, which combines stellar evolution with secular
evolution of triple systems, and explore how robust the predictions of these
simulations are under variations of uncertain initial conditions. We find that
interactions are common among massive triple stars. The majority of systems
(65-77\%) experience a phase of mass transfer in the inner binary, often with
an unevolved donor star. This differs significantly from isolated binary
evolution, where mass transfer is less frequent (52.3\% instead of 67\% for our
fiducial model) and the donors are typically post-main sequence stars. Initial
constraints for dynamical stability as well as eccentricity oscillations driven
by the third body facilitate the occurrence of interactions, for instance mass
transfer. The requirement of dynamical stability at formation places quite
stringent constraints on allowed orbital properties, reducing uncertainties in
triple evolution that resort from these initial conditions. Ignoring three-body
dynamics during evolution of non-interacting triples leads to triple
compact-object systems with stronger eccentricity oscillations and thereby
likely over-predicts the merger rate of compact objects in such systems.
