Aspect-based sentiment analysis (ABSA) has received increasing attention recently. Most existing work tackles ABSA in a discriminative manner, designing various task-specific classification networks for the prediction. Despite their effectiveness, these methods ignore the rich label semantics in ABSA problems and require extensive task-specific designs. In this paper, we propose to tackle various ABSA tasks in a unified generative framework. Two types of paradigms, namely annotation-style and extraction-style modeling, are designed to enable the training process by formulating each ABSA task as a text generation problem. We conduct experiments on four ABSA tasks across multiple benchmark datasets where our proposed generative approach achieves new state-of-the-art results in almost all cases. This also validates the strong generality of the proposed framework which can be easily adapted to arbitrary ABSA task without additional task-specific model design.