Component-based design is a different way of constructing systems which offers numerous benefits, in particular, decreasing the complexity of system design. However, deploying components into a system is a challenging and error-prone task. Model checking is one of the reliable methods that automatically and systematically analyses the correctness of a given system. Its brute-force check of the state space significantly expands the level of confidence in the system. Nevertheless, model checking is limited by a critical problem so-called Sate Space Explosion (SSE). To benefit from model checking, appropriate methods to reduce SSE, is required. In two last decades, a great number of methods to mitigate the state space explosion have been proposed which have many similarities, dissimilarities, and unclear concepts in some cases. This research, firstly, aims at present a review and brief discussion of the methods of handling SSE problem and classify them based on their similarities, principle and characteristics. Second, it investigates the methods for handling SSE problem in verifying Component-based system (CBS) and provides insight into CBS verification limitations that have not been addressed yet. The analysis in this research has revealed the patterns, specific features, and gaps in the state-of-the-art methods. In addition, we identified and discussed suitable methods to soften SSE problem in CBS and underlined the key challenges for future research efforts.