Recent advances in machine learning (ML) and the surge in computational power have opened the way to the proliferation of ML and Artificial Intelligence (AI) in many domains and applications. Still, apart from achieving good accuracy and results, there are many challenges that need to be discussed in order to effectively apply ML algorithms in critical applications for the good of societies. The aspects that can hinder practical and trustful ML and AI are: lack of security of ML algorithms as well as lack of fairness and explainability. In this paper we discuss those aspects and provide current state of the art analysis of the relevant works in the mentioned domains.