When relativistic heavy ions collide, they experience a rapid deceleration due to strong interaction forces between the colliding nuclei. In the process of deceleration, the initial kinetic energy of the ions gets transferred to a pre-equilibrium gluon-rich droplet, which subsequently thermalizes to a rapidly expanding fireball of quark-gluon plasma. Non-central collisions create plasma in a highly vortical (rotating) state, reflecting a large mechanical angular momentum carried by the initial nuclei. We discuss several topics related to accelerating and, separately, rotating (quark-)gluon matter, mainly based on the first-principle numerical simulations. We present the first numerical Monte Carlo results on the phase diagram of accelerating gluon plasma. We also point out the controversies in the current literature on the effect of vorticity on the phase diagram of QCD and discuss the negativity of the moment of inertia of the quark-gluon plasma in a narrow but phenomenologically interesting range of temperatures above the phase transition, violation Tolman-Ehrenfest law due to conformal anomaly and associated strong inhomogeneities of rotating plasma, as well as the signatures of an exotic negative Barnett (spin-vortical coupling) effect for gluons.
