Trapped-ion quantum computing is a promising approach for practical quantum computing (QC). This review discusses the current state of the field, focusing on the challenges in scaling trapped-ion systems while maintaining high-fidelity control and measurement. Trapped ions have demonstrated the ability to perform single-qubit and two-qubit gates with high fidelity, meeting most of DiVincenzo's criteria for quantum computing. However, scaling to larger numbers of ions remains a challenge due to issues such as decoherence, control errors, and the need for efficient control and measurement techniques. Trapped ions are typically confined using Paul traps or Penning traps, with Paul traps being more commonly used for quantum computing. These traps allow for the manipulation of individual ions through laser and microwave techniques, enabling high-fidelity quantum operations. The qubit states can be implemented using various internal states of the ions, such as hyperfine, Zeeman, fine-structure, or optical qubits, each with its own advantages and limitations. The main challenges in scaling trapped-ion systems include increasing the number of trapped ions while maintaining high-fidelity control and measurement, reducing decoherence and control errors, and developing efficient methods for controlling large numbers of ions. Recent efforts have focused on improving the scalability of trapped-ion systems through the development of new trap geometries, integrated photonics, and error correction techniques. Additionally, the integration of control components such as photonics and electronics into ion traps is essential for achieving scalable quantum computing. The review also discusses the potential applications of trapped-ion quantum computing, including near-term experiments with up to 100 ions and the long-term outlook for scalable quantum computing. The paper emphasizes the importance of addressing the remaining challenges in trapped-ion systems to achieve practical quantum computing. The review concludes that while trapped-ion systems have made significant progress, further research is needed to overcome the remaining challenges and realize scalable quantum computing.Trapped-ion quantum computing is a promising approach for practical quantum computing (QC). This review discusses the current state of the field, focusing on the challenges in scaling trapped-ion systems while maintaining high-fidelity control and measurement. Trapped ions have demonstrated the ability to perform single-qubit and two-qubit gates with high fidelity, meeting most of DiVincenzo's criteria for quantum computing. However, scaling to larger numbers of ions remains a challenge due to issues such as decoherence, control errors, and the need for efficient control and measurement techniques. Trapped ions are typically confined using Paul traps or Penning traps, with Paul traps being more commonly used for quantum computing. These traps allow for the manipulation of individual ions through laser and microwave techniques, enabling high-fidelity quantum operations. The qubit states can be implemented using various internal states of the ions, such as hyperfine, Zeeman, fine-structure, or optical qubits, each with its own advantages and limitations. The main challenges in scaling trapped-ion systems include increasing the number of trapped ions while maintaining high-fidelity control and measurement, reducing decoherence and control errors, and developing efficient methods for controlling large numbers of ions. Recent efforts have focused on improving the scalability of trapped-ion systems through the development of new trap geometries, integrated photonics, and error correction techniques. Additionally, the integration of control components such as photonics and electronics into ion traps is essential for achieving scalable quantum computing. The review also discusses the potential applications of trapped-ion quantum computing, including near-term experiments with up to 100 ions and the long-term outlook for scalable quantum computing. The paper emphasizes the importance of addressing the remaining challenges in trapped-ion systems to achieve practical quantum computing. The review concludes that while trapped-ion systems have made significant progress, further research is needed to overcome the remaining challenges and realize scalable quantum computing.