It was established that computerised form of testing began in the early 1970s. However, limited computer availability in addition to high costs of maintenance and other related challenges has caused serious hindrance to the full implementation of computer-based testing. In recent times, with the introduction of new technologies in teaching / learning process, computer-based testing has begun to be developed and implemented in large-scale testing programmes such as for certification, admissions, licensure as well as psychological testing situations. Despite numerous challenges associated with computer-based testing, universities and other tertiary institutions in Nigeria are shifting from the traditional paper-and-pen testing to the new computer-based testing. In this paper, the concept of computer-based testing was discussed, including the two major types. This was followed by the historical development of computer-based testing as well as the guidelines for computer-based testing as published by the Association of Test Publishers (ATP) in 2000. Advantages as well as the challenges of computer-based testing were later discussed, and the paper ended with a summary, conclusion and recommendation on how to make improvement in computer-based testing.