Enabling robust intelligence in the real-world entails systems that offer continuous inference while learning from varying amounts of data and supervision. The machine learning community has organically broken down this challenging goal into manageable sub-tasks such as supervised, few-shot, and continual learning. In light of substantial progress on each sub-task, we pose the question, How well does this progress translate to more practical scenarios? To investigate this question, we construct a new framework, FLUID, which removes certain assumptions made by current experimental setups while integrating these sub-tasks via the following design choices -- consuming sequential data, allowing for flexible training phases, being compute aware, and working in an open-world setting. Evaluating a broad set of methods on FLUID leads to new insights including strong evidence that methods are overfitting to their experimental setup. For example, we find that representative few-shot methods are substantially worse than simple baselines, self-supervised representations from MoCo fail to learn new classes when the downstream task contains a mix of new and old classes, and pretraining largely mitigates the problem of catastrophic forgetting. Finally, we propose two new simple methods which outperform all other evaluated methods which further questions our progress towards robust, real-world systems. Project page: https://raivn.cs.washington.edu/projects/FLUID/.