Title: Defining Benchmarks for Continual Few-Shot Learning. Abstract: In recent years there has been substantial progress in few-shot learning, where a model is trained on a small labeled dataset related to a specific task, and in continual learning, where a model has to retain knowledge acquired on a sequence of datasets. Both of these fields are different abstractions of the same real world scenario, where a learner has to adapt to limited information from different changing sources and be able to generalize in and from each of them. Combining these two paradigms, where a model is trained on several sequential few-shot tasks, and then tested on a validation set stemming from all those tasks, helps by explicitly defining the competing requirements for both efficient integration and continuity. In this paper we propose such a setting, naming it Continual Few-Shot Learning (CFSL). We first define a theoretical framework for CFSL, then we propose a range of flexible benchmarks to unify the evaluation criteria. As part of the benchmark, we introduce a compact variant of ImageNet, called SlimageNet64, which retains all original 1000 classes but only contains 200 instances of each one (a total of 200K data-points) downscaled to 64 by 64 pixels. We provide baselines for the proposed benchmarks using a number of popular few-shot and continual learning methods, exposing previously unknown strengths and weaknesses of those algorithms. The dataloader and dataset will be released with an open-source license.