Assembly systems (ASs) have moved into the era of mass customisation and Industry 4.0 (I4.0). Mass customisation involves a shift from the production of high quantities of the same product to the production of low quantities of a high number of different products. This is changing the way in which companies assemble their products and has introduced a certain number of challenges. For example, there are increases in the numbers of parts to be moved, the quantities of data to be collected, and the skills of the human workers that companies must manage to meet their customers' demand. The adoption of I4.0 technologies can help companies to face these challenges. However, although companies and researchers have studied possible solutions based on I4.0 technologies for ASs and have introduced the concept of Assembly System 4.0 (AS4.0), no studies have tried to understand how these technologies impact on decision areas at the strategic, tactical, and operational levels. In this paper, we attempt to fill this gap through a systematic literature review that not only offers the opportunity to understand the current situation and the state of the art in this field but also gives an overview of possible future research challenges.