In egocentric action recognition a single population model is typically trained and subsequently embodied on a head-mounted device, such as an augmented reality headset. While this model remains static for new users and environments, we introduce an adaptive paradigm of two phases, where after pretraining a population model, the model adapts on-device and online to the user's experience. This setting is highly challenging due to the change from population to user domain and the distribution shifts in the user's data stream. Coping with the latter in-stream distribution shifts is the focus of continual learning, where progress has been rooted in controlled benchmarks but challenges faced in real-world applications often remain unaddressed. We introduce EgoAdapt, a benchmark for real-world egocentric action recognition that facilitates our two-phased adaptive paradigm, and real-world challenges naturally occur in the egocentric video streams from Ego4d, such as long-tailed action distributions and large-scale classification over 2740 actions. We introduce an evaluation framework that directly exploits the user's data stream with new metrics to measure the adaptation gain over the population model, online generalization, and hindsight performance. In contrast to single-stream evaluation in existing works, our framework proposes a meta-evaluation that aggregates the results from 50 independent user streams. We provide an extensive empirical study for finetuning and experience replay.