Monitoring online customer reviews is important for business organisations to measure customer satisfaction and better manage their reputations. In this paper, we propose a novel dynamic Brand-Topic Model (dBTM) which is able to automatically detect and track brand-associated sentiment scores and polarity-bearing topics from product reviews organised in temporally-ordered time intervals. dBTM models the evolution of the latent brand polarity scores and the topic-word distributions over time by Gaussian state space models. It also incorporates a meta learning strategy to control the update of the topic-word distribution in each time interval in order to ensure smooth topic transitions and better brand score predictions. It has been evaluated on a dataset constructed from MakeupAlley reviews and a hotel review dataset. Experimental results show that dBTM outperforms a number of competitive baselines in brand ranking, achieving a good balance of topic coherence and uniqueness, and extracting well-separated polarity-bearing topics across time intervals.