Component-Based Software Engineering (CBSE) is becoming popular due to the benefits of software reusability and the availability of many alternatives of reusable components. By reusing existing software components that have already been tested, software engineers may reduce errors and shorten the time and cost to market the system under development. However, software engineers still have a problem in selecting the existing reusable components as well as difficulties in determining the quality of the developed components for future reuse. Therefore, an appropriate component selection process is extremely needed to harvest the full benefits of software reuse. In this paper, the software component selection is reviewed in detail however the emphasize is given on the problems that occur in component selection. Firstly the component based software development is considered, followed by component selection problem in general (simple component selection problem) and (criteria based component selection).Subsequently, the authors analyzed about ten papers in terms of the major problem, proposed solution and critical analysis. In the end conclusion is drawn based on critical analysis the authors highlights the various factors(Considering non-functional factors, dynamic requirements, formal specification for component repositories, fuzzy theory for subjective judgments) that must be taken into consideration to improve the component selection process.