Adapting Automatic Speech Recognition (ASR) models to new domains leads to Catastrophic Forgetting (CF) of previously learned information. This paper addresses CF in the challenging context of Online Continual Learning (OCL), with tasks presented as a continuous data stream with unknown boundaries. We extend OCL for ASR into the unsupervised realm, by leveraging self-training (ST) to facilitate unsupervised adaptation, enabling models to adapt continually without label dependency and without forgetting previous knowledge. Through comparative analysis of various OCL and ST methods across two domain adaptation experiments, we show that UOCL suffers from significantly less forgetting compared to supervised OCL, allowing UOCL methods to approach the performance levels of supervised OCL. Our proposed UOCL extensions further boosts UOCL's efficacy. Our findings represent a significant step towards continually adaptable ASR systems, capable of leveraging unlabeled data across diverse domains.