We study the problem of response selection for multi-turn conversation in retrieval-based chatbots. The task involves matching a response candidate with a conversation context, the challenges for which include how to recognize important parts of the context, and how to model the relationships among utterances in the context. Existing matching methods may lose important information in contexts as we can interpret them with a unified framework in which contexts are transformed to fixed-length vectors without any interaction with responses before matching. This motivates us to propose a new matching framework that can sufficiently carry important information in contexts to matching and model relationships among utterances at the same time. The new framework, which we call a sequential matching framework (SMF), lets each utterance in a context interact with a response candidate at the first step and transforms the pair to a matching vector. The matching vectors are then accumulated following the order of the utterances in the context with a recurrent neural network (RNN) that models relationships among utterances. Context-response matching is then calculated with the hidden states of the RNN. Under SMF, we propose a sequential convolutional network and sequential attention network and conduct experiments on two public data sets to test their performance. Experiment results show that both models can significantly outperform state-of-the-art matching methods. We also show that the models are interpretable with visualizations that provide us insights on how they capture and leverage important information in contexts for matching.