Conversational question answering (ConvQA) is a simplified but concrete setting of conversational search . One of its major challenges is to leverage the conversation history to understand and answer the current question. In this work, we propose a novel solution for ConvQA that involves three aspects. First, we propose a positional history answer embedding method to encode conversation history with position information using BERT  in a natural way. BERT is a powerful technique for text representation. Second, we design a history attention mechanism (HAM) to conduct a “soft selection” for conversation histories. This method attends to history turns with different weights based on how helpful they are on answering the current question. Third, in addition to handling conversation history, we take advantage of multi-task learning (MTL) to do answer prediction along with another essential conversation task (dialog act prediction) using a uniform model architecture. MTL is able to learn more expressive and generic representations to improve the performance of ConvQA. We demonstrate the effectiveness of our model with extensive experimental evaluations on QuAC, a large-scale ConvQA dataset. We show that position information plays an important role in conversation history modeling. We also visualize the history attention and provide new insights into conversation history understanding.