Advances in machine learning (ML) open the way to innovating functions in the avionic domain, such as navigation/surveillance assistance (e.g. vision-based navigation, obstacle sensing, virtual sensing), speechto-text applications, autonomous flight, predictive maintenance or cockpit assistance. Current certification standards and practices, which were defined and refined decades over decades with classical programming in mind, do not however support this new development paradigm. This article provides an overview of the main challenges raised by the use ML in the demonstration of compliance with regulation requirements, and a survey of literature relevant to these challenges, with particular focus on the issues of robustness and explainability of ML results.