## 1 Introduction
With obvious benefits, integrating DT into CPS could pose numerous challenges to modeling, computing, networking, and data analysis, alongside the exceptional requirements of CPS with respect to latency, reliability, safety, scalability, security, and privacy, among others. While advanced networking, computing, and data analysis technologies can help the realization of DT, there are a number of issues that need to be addressed, including how to define the theoretical foundation and modeling techniques such that DT accurately and reliably reflect the states of things, how to design ML/DL models to achieve real-time big data processing, and and how to secure DT and protect privacy-sensitive information collection and publishing. There are some existing studies that have proposed feasible approaches, such as leveraging multi-domain and multi-level designs in manufacturing systems; that is, designs based on different sub-system digital abstractions in different domains, and designs based on the principal structures of real physical systems at different levels [33]. In order to ensure that DT can represent the physical systems precisely, the multi-domain and multi-level design process must accompany the life-cycle of real physical systems. In addition, some existing surveys summarize existing DT efforts that are designed to emulate real physical systems. For example, there are several existing surveys focusing on inspectingthe framework of DT in industrial systems [30; 34; 35; 36]. Additionally, some studies have focused on categorizing different DTs in the power grid [37; 38; 39; 40]. Nonetheless, since IoT is widely applied to different physical systems, it is necessary to conduct a comprehensive investigation of extending DTs to IoT-based smart systems driven by data science and engineering. Furthermore, based on new techniques, the challenges and future research directions for DT need to be discussed. To address the aforementioned problems and issues, we make the following contributions in this study. * We begin with the architecture design of existing DTs, which includes DT variants, DT sub-types, and IoT-based DT. We then review the data representation and communication protocols for DT. In addition, we present the use cases for applying DT into a variety of smart-world systems, which include smart grid, smart transportation, smart city, and smart manufacturing, as typical CPS. * Based on the architecture and its applications to smart-world systems, we discuss challenges that arise from four perspectives: CPS, data science, optimization, and security and privacy. We also present several research directions for DT that we strongly feel need further research, including performance, new DT-driven services, modeling and machine learning, and security and privacy. The remainder of this paper is organized as follows: In Section 2, we provide the historical background of DT, including the key concepts, techniques, architecture, and protocols of DT. In Section 3, we review the examples of applying DT into smart-world systems, including smart grid, smart transportation, smart manufacturing, and smart cities as case study. In Section 4, we present the challenges of DT from the perspectives of CPS, data science, optimization, and security and privacy. In Section 5, we outline possible future research directions from the perspectives of performance, new DT-driven services, modeling and machine learning, and security and privacy. Finally, we summarize the paper in Section 6.