Context: Machine Learning (ML) has been at the heart of many innovations over the past years. However, including it in so-called “safety-critical” systems such as automotive or aeronautic has proven to be very challenging, since the shift in paradigm that ML brings completely changes traditional certification approaches. Objective: This paper aims to elucidate challenges related to the certification of ML-based safety-critical systems, as well as the solutions that are proposed in the literature to tackle them, answering the question “How to Certify Machine Learning Based Safety-critical Systems?”. Method: We conduct a Systematic Literature Review (SLR) of research papers published between 2015 and 2020, covering topics related to the certification of ML systems. In total, we identified 217 papers covering topics considered to be the main pillars of ML certification: Robustness, Uncertainty, Explainability, Verification, Safe Reinforcement Learning, and Direct Certification. We analyzed the main trends and problems of each sub-field and provided summaries of the papers extracted. Results: The SLR results highlighted the enthusiasm of the community for this subject, as well as the lack of diversity in terms of datasets and type of ML models. It also emphasized the need to further develop connections between academia and industries to deepen the domain study. Finally, it also illustrated the necessity to build connections between the above mentioned main pillars that are for now mainly studied separately. Conclusion: We highlighted current efforts deployed to enable the certification of ML based software systems, and discuss some future research directions.