Pathology imaging is broadly used for identifying the causes and effects of diseases or injuries. Given a pathology image, being able to answer questions about the clinical findings contained in the image is very important for medical decision making. In this paper, we aim to develop a pathological visual question answering framework to analyze pathology images and answer medical questions related to these images. To build such a framework, we create PathVQA, a pathology VQA dataset with 32,795 questions asked from 4,998 pathology images. We also propose a three-level optimization framework which performs self-supervised pretraining and VQA finetuning end-to-end to learn powerful visual and textual representations jointly and automatically identifies and excludes noisy self-supervised examples from pretraining. We perform experiments on our created PathVQA dataset and the results demonstrate the effectiveness of our proposed methods. The datasets and code are available at https://github.com/UCSD-AI4H/PathVQA.