In order for businesses to respond to new and emerging technologies, secure future growth and stay competitive in disruptive market shifts, they may employ innovative business models. Businesses of all sizes, ages and from all industries are acting more entrepreneurially by initiating innovative changes to their existing business models or introducing completely new business models to respond to these disruptions. In recent years, researchers and practitioners have paid more attention to the topic of business model innovation (BMI), with literature focusing on BMI as a transformation and renewal opportunity. Over the past few years, the process of successfully achieving and fostering BMI has been researched; however, we have identified a research gap in terms of a lack of systematic guidelines for what is required to achieve BMI and how this can be done. Furthermore, previous studies have mainly focused on large businesses and not small and medium-sized enterprises (SMEs), which are regarded as the driving force of most economies. This study adopted a qualitative research approach by systematically reviewing existing BMI processes. The guiding research question of this study is: How can SMEs achieve BMI? To answer this research question, the review focused on the activities, steps and tools needed to successfully realise BMI. Besides providing an overview on the process of achieving BMI success, special attention was placed on how these processes have been adapted over the last decade to accommodate the opportunities presented by technology and digitalisation within the Fourth Industrial Revolution in which businesses find themselves today. The results indicate that the most common BMI frameworks are the Business Model Canvas, the St. Gallen Business Model Navigator and the Cambridge business model innovation framework. Additionally, only a few studies incorporate digital technologies as a single dimension into the BMI framework, which is identified as a major gap in the literature. This paper contributes to the body of knowledge on BMI processes and outlines how SMEs can successfully achieve BMI in light of the Fourth Industrial Revolution. The topic is in need of additional insight and development, and recommendations for future research are thus provided.