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Effort estimation of software development is an important sub-discipline in software engineering. It has been the focus of much research mostly over the last couple of decades. In recent years, software development turned into engineering through the introduction of component-based software development (CBSD). The industry has reported significant advantages in using CBSD over traditional software development paradigms. However, the introduction of CBSD has also brought a host of unique challenges to software effort estimation which are quite different from those associated with traditional software development. Owing to the increasing tendency to use the CBSD approach in recent years, it is clear that effort estimation of CBSD is particularly an important area of research with a direct relevance to industry. In this study, the authors survey the most up-to-date research work published on predicting the effort of CBSD. The authors analyse the surveyed approaches in terms of modelling technique, the type of data required for their use, the type of estimation provided, lifecycle activities covered and their level of acceptability with regard to any validation. The aim of this survey is to provide a better understanding of the cost and schedule estimation approaches for CBSD.