Although learning analytics dashboards (LAD) grow in numbers, they often fail to improve learner awareness as they lack adaptation capabilities. This paper presents a systematic review following the PRISMA statement, about the adaptation capabilities of LADs based on new definitions for LADs and learning indicators. A detailed analysis of 23 articles selected among 426 articles retrieved from databases was conducted based on a coding scheme, centered on adaptation and its dimensions, namely: to whom, what, to what, who, and how. The main result of this study is that there is more evidence of adaptable LADs than adaptive LADs. As a result, the road to adaptivity is worth exploring. The analysis of LAD's common features led us to distinguish mainly 4 adaptable capabilities and 2 adaptive ones. Most of the adaptable capabilities consist of giving exploration power to the user and providing him with data filtering, zooming, or selection functionalities. In contrast, users have limited options when it comes to selecting indicators, their visualizations, and organization on the dashboard. Providing more flexible LADs could enhance their usability and increase learner awareness. Furthermore, the few adaptive features involve adaptations based on "if-then" rules and there are no reports of advanced computing techniques such as machine learning that could empower LAD's adaptation.