Despite the many studies on physical and physiological features of combat sport athletes, there has been considerably less consideration of psychological factors. Here, we present a narrative review of literature related to perceptual-cognitive skill in combat sports that require the athlete to score points by hitting or touching the opponent's body with the hands, feet or weapon: boxing, French boxing, fencing, kung fu (wushu), karate, taekwondo and other martial arts. Based on a thorough search of literature, we synthesised findings from empirical studies on Reaction Time, Anticipation, Visual Search and Information Pick-up. Contrary to the belief of coaches, there was no clear consensus regarding Reaction Time being a good predictor of success in combat sports. However, consistent with findings from other sports, expert combat sport athletes better anticipate the opponent's actions based on information perceived before and during the attack. This is likely facilitated by experts using a gaze fixation strategy (i.e., visual pivot) that facilitates information pick-up. In the final section, we present a model that describes how the evolving perception-action relationship between the attacking athlete and opponent depends on distance, attack progression and opponent reaction. Suggestions are provided for training and for future research in combat sports.