This study presents a 13-year (2006-2018) systematic literature review related to the way that computational thinking (CT) has grown in elementary level education students (K-6) with the intention to: (a) present an overview of the educational context/setting where CT has been implemented, (b) identify the learning context that CT is used in education, (c) highlight the ways of assessment/measurement of CT and present the learning outcomes for students who engage in CT educational activities. A set of criteria were specified to select appropriate studies for inclusion in the review. A thorough search in ten large electronic databases, meeting the inclusion criteria, revealed 53 studies on CT in primary education. The results of the study revealed a variety of educational and learning contexts that CT has been integrated. The majority of studies use the framework of programming for both plugged and unplugged activities in order to cultivate students' CT-skills, while the main interest focuses on the subject of Computer Science and STEM field in general. However, teaching and learning issues on CT-concepts and skills, CT-measurement and the adoption of an established definition of CT remain a challenge. Based on the current findings, some recommendations and implications for future research are provided.