This paper presents an original study with the aim of propose and test a machine learning approach to research about employability and employment. To understand how the graduates get employed, researchers propose to build predictive models using machine learning algorithms, extracting after that the most relevant factors that describe the model and employing further analysis techniques like clustering to get deeper insights. To test the proposal, is presented a case study that involves data from the Spanish Observatory for Employability and Employment (OEEU). Using data from this project (information about 3000 students), has been built predictive models that define how these students get a job after finalizing their degrees. The results obtained in this case study are very promising, and encourage authors to refine the process and validate it in further research.