Thanks to the increasing availability of granular, yet high-dimensional, firm level data, machine learning (ML) algorithms have been successfully applied to address multiple research questions related to firm dynamics. Especially supervised learning (SL), the branch of ML dealing with the prediction of labelled outcomes, has been used to better predict firms' performance. In this contribution, we will illustrate a series of SL approaches to be used for prediction tasks, relevant at different stages of the company life cycle. The stages we will focus on are (i) startup and innovation, (ii) growth and performance of companies, and (iii) firms exit from the market. First, we review SL implementations to predict successful startups and R&D projects. Next, we describe how SL tools can be used to analyze company growth and performance. Finally, we review SL applications to better forecast financial distress and company failure. In the concluding Section, we extend the discussion of SL methods in the light of targeted policies, result interpretability, and causality.