The thesis presents a systematic literature review covering the implementation of the Kanban approach within the field of software development. The first section provides background related to the research area by describing lean software development, the Kanban method and the guidelines for undertaking such a review. The second section covers the article The kanban approach, between agility and leanness: a systematic review which is a systematic literature review of research studies on the implementation of the Kanban approach in the process of software development, published between 1990 and 2012. The purpose of the article was to illuminate the guiding principles and elements of the Kanban approach in order to increase the likelihood of implementing it successfully by defining the prime elements of Kanban and outlining the advantages and benefits of using it within IT organisations. The results of the systematic literature review are presented in the third section. The analysis was conducted following the guidelines from the first section, covering scientific writings published after 2012. The final section presents the findings of the systematic literature review and their comparison to the findings from the above-mentioned article.