Answer selection, which is involved in many natural language processing applications such as dialog systems and question answering (QA), is an important yet challenging task in practice, since conventional methods typically suffer from the issues of ignoring diverse real-world background knowledge. In this paper, we extensively investigate approaches to enhancing the answer selection model with external knowledge from knowledge graph (KG). First, we present a context-knowledge interaction learning framework, Knowledge-aware Neural Network (KNN), which learns the QA sentence representations by considering a tight interaction with the external knowledge from KG and the textual information. Then, we develop two kinds of knowledge-aware attention mechanism to summarize both the context-based and knowledge-based interactions between questions and answers. To handle the diversity and complexity of KG information, we further propose a Contextualized Knowledge-aware Attentive Neural Network (CKANN), which improves the knowledge representation learning with structure information via a customized Graph Convolutional Network (GCN) and comprehensively learns context-based and knowledge-based sentence representation via the multi-view knowledge-aware attention mechanism. We evaluate our method on four widely-used benchmark QA datasets, including WikiQA, TREC QA, InsuranceQA and Yahoo QA. Results verify the benefits of incorporating external knowledge from KG, and show the robust superiority and extensive applicability of our method.