Title: Continual Active Learning. Abstract: While active learning (AL) improves the labeling efficiency of machine learning (by allowing models to query the labels of data samples), a major problem is that compute efficiency is decreased since models are typically retrained from scratch at each query round.  In this work, we develop a new framework that circumvents this problem by biasing further training towards the recently labeled sets, thereby complementing existing work on AL acceleration. We employ existing and novel replay-based Continual Learning (CL) algorithms that are effective at quickly learning new samples without forgetting previously learned information, especially when data comes from a shifting or evolving distribution. We call this compute-efficient active learning paradigm $\textit{``Continual Active Learning" (CAL)}$. We demonstrate that standard AL with warm starting fails, both to accelerate training, and that naive fine-tuning suffers from catastrophic forgetting due to distribution shifts over query rounds.  We then show CAL achieves significant speedups using a plethora of replay schemes that use model distillation, and that select diverse/uncertain points from the history, all while maintaining performance on par with standard AL.  We conduct experiments across many data domains, including natural language, vision, medical imaging, and computational biology, each with very different neural architectures (Transformers/CNNs/MLPs). CAL consistently provides a 2-6x reduction in training time, thus showing its applicability across differing modalities.