Most benchmarks for studying surgical interventions focus on a specific challenge instead of leveraging the intrinsic complementarity among different tasks. In this work, we present a new experimental framework towards holistic surgical scene understanding. First, we introduce the Phase, Step, Instrument, and Atomic Visual Action recognition (PSI-AVA) Dataset. PSI-AVA includes annotations for both long-term (Phase and Step recognition) and short-term reasoning (Instrument detection and novel Atomic Action recognition) in robot-assisted radical prostatectomy videos. Second, we present Transformers for Action, Phase, Instrument, and steps Recognition (TAPIR) as a strong baseline for surgical scene understanding. TAPIR leverages our dataset's multi-level annotations as it benefits from the learned representation on the instrument detection task to improve its classification capacity. Our experimental results in both PSI-AVA and other publicly available databases demonstrate the adequacy of our framework to spur future research on holistic surgical scene understanding.