With the rapid growth of technology enhanced learning, new mediums for learning have emerged. One of these mediums is computer based learning where the main concern is how to design a computer based learning system which takes into consideration the learners differences. Personality is considered as one of the most critical sources of individual differences. This study investigates how personality differences within learners can affect computer based learning, through a comprehensive review of the literature. The highlighted results from the obtained nineteen studies are: (a) the most referred to personality model in computer based learning is MBTI; (b) personality traits affect how learners prefer learning content and learning approach like collecting information, communicating with instructor and peer, study behavior, acting and performing; (c) a new model of personality variables should be considered in computer based learning by taking all interested researchers and practitioners into accounts; and (d) the traditional questionnaire approach which is still the pre-dominant method to identify the learner s personality; and this needs to be changed with new potential of big data and learning analytics. Furthermore, this study presents a new implicit approach using learning analytics instead of questionnaire-based approach to identify the learners personality.