Currently, Higher Education Institutions (HEIs) and companies around the world are experiencing a renewed interest in strengthening their forms of cooperation. There are many benefits to be gained by boosting this partnership. Employment opportunities, exchange of knowledge and the development of new teaching and learning methodologies are direct advantages for all those involved in this cooperation. This paper presents an overview of the existing cooperation models between different actors: HEIs student-company and HEIs expert-company. In addition, models where companies are directly involved in HEI education are also searched and analysed. It is to be noted that this work is framed within the context of the Smart HEI-Business collaboration for skills and competitiveness (HEIBus) project. The HEIBus is an Erasmus + Knowledge Alliances 2 (KA2) project with a budget of about one million euros and a duration of 36 months. Five European universities and seven companies with strong expertise and experience in different fields are taking part in this project. HEIBus focuses on strengthening the collaboration between HEIs and companies by creating new innovative cooperation models. These models are also detailed in this work.