The Digital Twin paradigm is a very promising technology that can be applied to various fields and applications. However, it lacks a unifying framework for classifying and defining use cases. The goal of this paper is to address the identified gap. Using a field study and a bottom-up approach, it aims to categorize the various uses of the industrial Digital Twin to help formalize the concept and rationalize its adoption by a range of industrial sectors. The study is based on an iterative process of collecting use cases from a wide variety of verticals, applying grounded theory principles. The usage scenarios were extracted, synthesized, grouped and abstracted to develop an actionable use cases classification framework. This article presents the resulting taxonomy and illustrates it by detailing real industrial use cases, including their value proposition and application areas. This collection, classification and analysis of use cases led to a study of the common aspects proposed in academic and industrial definitions of the Digital Twin. The goal was to combine and generalize these aspects into a pragmatic and unifying definition, on which the Alliance for Industry of the Future (AIF) committee has converged. The main contributions of this work include proposing, from a joint industrial and academic perspective, (i) the first domain-independent and industry-focused systematic collection of Digital Twin use cases, (ii) a comprehensive framework for analyzing and classifying Digital Twin use cases and their requirements, and (iii) a consensual general definition of the industrial Digital Twin to contribute to the structuring and standardization of this very active ecosystem. •Industrial Digital Twin use cases have been collected, analyzed, and summarized.•A first framework for classifying industrial Digital Twin use cases is proposed.•An analysis guide shows how the Digital Twins are used in industry.•A set of Digital Twins definitions have been analyzed and classified.•A consensual, pragmatic and unifying Digital Twin definition is proposed.