Emotions are one of the important subconscious mechanisms that influence human behaviors, attentions, and decision making. The emotion process helps to determine how humans perceive their internal status and needs in order to form consciousness of an individual. Emotions have been studied from multidisciplinary perspectives and covered a wide range of empirical and psychological topics, such as understanding the emotional processes, creating cognitive and computational models of emotions, and applications in computational intelligence. This paper presents a comprehensive survey of cognitive and computational models of emotions resulted from multidisciplinary studies. It explores how cognitive models serve as the theoretical basis of computational models of emotions. The mechanisms underlying affective behaviors are examined as important elements in the design of these computational models. A comparative analysis of current approaches is elaborated based on recent advances towards a coherent cognitive computational model of emotions, which leads to the machine simulated emotions for cognitive robots and autonomous agent systems in cognitive informatics and cognitive computing.