The Autonomous Air Combat technique has been a lasting research topic for decades. However, no complete solutions seem to have appeared because of the highly dynamic and complex nature of the Autonomous Air Combat problem. In devising the Autonomous Air Combat solutions, we follow similar methodologies in the robotics community, and divide the overall scheme into two folds: the perception of other (enemy/friendly) aircraft, and the guidance/control for own aircraft. While the perception in the first fold serves as a foundation, this paper is mainly focused on the second one. Based on our survey, a review of own aircraft guidance/control in the (primarily one-to-one) Autonomous Air Combat solutions is presented. We divide different Autonomous Air Combat solutions into three groups, i.e. mathematics-based, knowledge-encoded, and learning-driven. In each group, we present the representative methods first; problem definition, solution, and a brief overview of the historical development are illustrated. We also comment on both weakness and strengths for each group/method. We point out certain technical paths/challenges that need to be addressed in the future Autonomous Air Combat development, i.e. to abstract and emulate the human pilot experiences, and to develop the online learning capabilites. Inspired by the state-of-art techniques in other similar fields (robotics, autonomous driving), we also propose potential solutions, i.e. traditional approaches enhanced by the novel data-driven technique. Via this paper, we hope to deliver an in-depth analysis of past experiences and potential challenges/solutions for the Autonomous Air Combat technique. We also advocate referring to the approaches/techniques that are utilized in other similar fields in devising the Autonomous Air Combat solutions.