In recent years, the hype around Digital Twins (DTs) has been exponentially increasing in both industry and academia. DTs are a potential solution to increase automation and advance towards Smart Manufacturing. Manufacturing DTs have been implemented at different hierarchical levels, ranging from system of systems to unit level. Increasing computational capacity and data exchange rates can enable DT implementations for real-time applications. Several literature reviews on manufacturing DTs have been published. However, no previous paper focuses on manufacturing DTs at the unit level for which real-time control is most applicable. Simultaneously, the challenges to engineer DTs with real-time capabilities are enormous, both from a scientific and technological perspective. Therefore, we focus on DTs of single production units such as traditional machine tools, additive manufacturing machines and advanced robotic applications. In this systematic literature review, 96 papers about practical unit level DT applications found in the Scopus database using a combination of the keywords “Digital Twin”, “Production” and “Manufacturing” are reviewed. We summarize how DTs are currently implemented and operated, and what potential benefits DTs offer at the unit process level in four categories: generic reference models, services, DT content (models and data) and DT deployment (hardware and software). Following the thematic analysis, an overall discussion, summary of key contributions and identified research gaps, and outlook into future research avenues is given. Key findings of this review can be summarized as: focus on DT components versus being holistic; need to share data and models across multiple stakeholders; lack of physical fidelity of the models; stark contrast of lab scale developments and real world testing, e.g., historical data and storage related challenges; lack of clear definition of DT in industry, and missing semantic interoperability between a wide variety of domains.