Observations of cosmic rays and broadband radiation spectra imply the prevalence of relativistic particles in high-energy astrophysical systems (such as black-hole accretion flows and jets). Turbulence is a leading candidate process for energizing these particles, but has long been challenging to model due to the complicated, multi-scale nonlinear dynamics of collisionless plasmas. Particle-in-cell (PIC) simulations of relativistic (and trans-relativistic) turbulence have recently opened this topic to rigorous, first-principles numerical scrutiny. I will describe recent progress on understanding turbulent plasma energization in high-energy astrophysical regimes. PIC simulations demonstrate efficient turbulent particle acceleration and confirm its diffusive nature, while also yielding new insights into the electron-to-ion heating ratio and radiative signatures. However, modeling the power-law energy distribution of accelerated particles requires stepping beyond standard frameworks; I will describe theoretical efforts to model particle acceleration with generalized maximum entropy principles. The next several years promise to bring fundamental breakthroughs to this frontier of plasma astrophysics.