Benefiting from quantum superposition and quantum entanglement, quantum computing offers significant computational speedup over classical counterparts for certain classes of complex problems. Ion trap is one of the leading physical platforms for realizing universal quantum computing. High-fidelity elementary quantum operations above the fault-tolerant threshold in small-scale systems have been demonstrated, such as state preparation and measurement, and universal quantum gates. Scaling trapped-ion systems to larger qubit counts while maintaining high fidelity is a central challenge and a key research direction toward practical quantum computing. This article begins with an overview of the principles of quantum parallel computing and historical development of quantum computing, which is followed by a comprehensive discussion of the foundational concepts and recent progress in ion trap quantum computing from the perspectives of hardware architecture and computing principles. Then, it focuses on the critical issue of scaling, reviewing mainstream approaches such as ion transport and ion-photon quantum networks, along with their current limitations. Furthermore, it explores emerging strategies for scaling, including the development of two-dimensional ion crystal. Finally, the article provides recommendations to accelerate the advancement of quantum computing from both technological and industrial perspectives.