Trapped ions are a promising platform for practical quantum computing (QC) due to their robustness, long coherence times, and strong ion-ion interactions. This review covers the basics of trapped ion QC, including the strengths and limitations of trapped ions as qubits, and discusses recent progress and challenges in scaling up trapped-ion quantum computers while mitigating decoherence and control errors. The authors highlight the importance of modular and monolithic integration, error correction, and connectivity in achieving scalability. They also explore near-term applications and the outlook for trapped-ion QC, emphasizing the need for further research to overcome remaining challenges. Key topics include ion trapping methods, qubit states, and control techniques, with a focus on the practical aspects of scaling and error mitigation.Trapped ions are a promising platform for practical quantum computing (QC) due to their robustness, long coherence times, and strong ion-ion interactions. This review covers the basics of trapped ion QC, including the strengths and limitations of trapped ions as qubits, and discusses recent progress and challenges in scaling up trapped-ion quantum computers while mitigating decoherence and control errors. The authors highlight the importance of modular and monolithic integration, error correction, and connectivity in achieving scalability. They also explore near-term applications and the outlook for trapped-ion QC, emphasizing the need for further research to overcome remaining challenges. Key topics include ion trapping methods, qubit states, and control techniques, with a focus on the practical aspects of scaling and error mitigation.