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The quality of learned features by representation learning determines the performance of learning algorithms and the related application tasks (such as high-dimensional data clustering). As a relatively new paradigm for representation learning, Concept Factorization (CF) has attracted a great deal of interests in the areas of machine learning and data mining for over a decade. Lots of effective CF based methods have been proposed based on different perspectives and properties, but note that it still remains not easy to grasp the essential connections and figure out the underlying explanatory factors from exiting studies. In this paper, we therefore survey the recent advances on CF methodologies and the potential benchmarks by categorizing and summarizing the current methods. Specifically, we first re-view the root CF method, and then explore the advancement of CF-based representation learning ranging from shallow to deep/multilayer cases. We also introduce the potential application areas of CF-based methods. Finally, we point out some future directions for studying the CF-based representation learning. Overall, this survey provides an insightful overview of both theoretical basis and current developments in the field of CF, which can also help the interested researchers to understand the current trends of CF and find the most appropriate CF techniques to deal with particular applications.