This paper provides an in-depth analysis of computational thinking (CT) skills and their assessment. It discusses the definition and components of CT. Various assessment tools, such as surveys, exams, self-assessment instruments, and performance tests, are explored. A bibliometric analysis reveals a growing trend in publications related to CT skills since 1993. The study employs citation analysis, co- citation analysis, and co-keyword analysis, identifying clusters of related work and emphasizing the core ideas of CT skills, their components, and their assessment. The findings highlight the intellectual synergy between publications, particularly the strong conceptual and thematic links between works that often cite each other. The discussion underscores the importance of CT components like abstraction, decomposition, and algorithms, as foundational elements across disciplines, particularly in education and computer science. Additionally, the integration of CT into educational curricula, such as robotics, programming, and STEM, demonstrates its growing significance. The conclusion identifies several gaps in the current understanding of CT, particularly the need for a standardized, widely accepted definition that encompasses all aspects of CT. It also emphasizes the limited focus on the assessment of CT skills and calls for the development of validated and reliable assessment tools. Furthermore, the paper highlights the need for more research on the impact of teacher training programs on CT development, to ensure effective integration at the school level.