This chapter delves into the concepts of quantum computers and their potential breakthrough applications for industry and society. The chapter provides the historical background to the development of digital computers and their economic benefits, and the need for quantum computers. The chapter explains how quantum computers work, outlines key hardware modalities, and highlights challenges in engineering scalable, fault-tolerant systems and designing effective quantum algorithms. The chapter outlines real-world case studies of firms experimenting with prototype quantum computers to solve business problems including simulation, optimisation, and pattern recognition for machine learning applications. The chapter also discusses the possible business and economic implications of quantum computing and identifies research questions for further exploration.