The manufacturing sector is experiencing a technological paradigm shift, where new information technology (IT) concepts can help digitize product design, production systems, and manufacturing processes. One of such concepts is Digital Twin and researchers have made some advancement on both its conceptual development and technological implementations. However, in practice, there are many different definitions of the digital-twin concept. These different definitions have created a lot of confusion for practitioners, especially small- and medium-sized enterprises (SMEs). Therefore, the adoption and implementation of the digital-twin concept in manufacturing have been difficult and slow. In this paper, we report our findings from a survey of companies (both large and small) regarding their understanding and acceptance of the digital-twin concept. Five supply-chain companies from discrete manufacturing and one trade organization representing suppliers in the automotive business were interviewed. Their operations have been studied to understand their current digital maturity levels and articulate their needs for digital solutions to stay competitive. This paper presents the results of the research including the viewpoints of these companies in terms of opportunities and challenges for implementing digital twins.