In Agile software delivery, complexity factors have become an important part that has been linked to the success of software projects, especially with highly structured plan-driven approaches. Although there are a range of known techniques, practices and structures aimed at improving communication, team, and organisational cohesion, there remains a poor understanding of how organisations and teams can effectively deal with complexity in Agile software delivery. While theoretical and management frameworks of complexity exist, nevertheless, little is known about the important complexity factors at play in the planning, design, and creation of Agile software at the various levels of organisational structures. To better understand complexity and how it may impact Agile delivery across organisational structures, processes and roles, a systematic literature review was undertaken to identify the known complexity factors, to identify gaps in our knowledge, and to identify the approaches that have been undertaken to date to address complexity. This review contributes a fresh perspective to the literature on complexity in Agile software delivery and forwards our conversation on complexity in IT projects, and their effective management. The review was structured around Remington and Pollack’s (2016) model identifying different types of complexity. The review’s findings indicate that complexities result from aspects in functional teams, organizational structures, roles, Agile tasks, and practice-related issues that were identified in distributed Agile projects. We conclude that there may remain a lack of understanding in practice of the complexity factors that are at play in an Agile software delivery context. These findings are relevant to researchers and practitioners seeking to identify areas of focus for addressing complexity in Agile software delivery.