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Concept-cognitive learning (CCL), an emerging intelligence learning paradigm, has recently become a popular research subject in artificial intelligence and cognitive computing. A central notion of CCL is cognitive and learning things via concepts. In this process, concepts play a fundamental role when mining and fusing knowledge from data to wisdom. With the in-depth research and expansion of CCL in scopes, goals, and methodologies, some difficulties have gradually emerged, including some vague terminology, ambiguous views, and scattered research. Hence, a systematic and comprehensive review of the development process and advanced research about CCL is particularly necessary at the moment. This paper summarizes the theoretical significance, application value, and future development potential of CCL. More importantly, by synthesizing the reviewed related research, we can acquire some interesting results and answer three essential questions: (1) why examine a cognitive and learning framework based on concept? (2) what is the concept-cognitive learning? (3) how to make concept-cognitive learning? The findings of this work could act as a valuable guide for related studies in quest of a clear understanding of the closely related research issues around concept-cognitive learning. • It is the first paper that attempts to provide an in-depth analysis of the advancement of CCL. • It is a multi-view categorization of CCL in research scopes, goals, and methodologies. • It is an elucidation of the main research gaps and suggestions for the related study of CCL. • It acquires some interesting results by synthesizing the reviewed related research of CCL. [ABSTRACT FROM AUTHOR]