Component Based Software Engineering (CBSE) is used to develop software from Commercial Off the Shelf Components (COTs) with minimum cost and time. Component Based Software Cost Estimation (CBSCE) is an important pre-development activity for the successful planning and cost estimation of Components-Based Software Development (CBSD) that saves cost and time. Many researchers are putting their efforts to propose and then develop a CBSCE model. This motivates to review research work and history of CBSCE from 1965 to 2023. The scope of this research also, to some extent, includes auxiliary the review of all the research work done in the areas such as CBSE, CBSCE, Component Based Software Metrics, COTs, component based process models to cover all the areas of CBSD under CBSE either to answer or to provide pointers for the answers to the questions of this area easily. Internet based search methodology has been used to review the available and published literature. This paper may also classify available literature of this area into its sub areas such as component selection, quality with chronological contribution of the researchers and pictorial presentation of its history. Thus this research paper may serve as a common source of information for the concerned researchers.
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