The rapid development of machine drive systems is closely tied to advancements in signal sampling technology. Accurate measurement results, especially current measurement results, are crucial for high-performance machine drive systems. However, current measurement errors (CME) caused by circuit parameter inconsistencies, aging, and temperature variations can significantly affect the control performance of drive systems, thus necessitating compensation. To better understand the mechanisms of CME in drive systems, this paper reviews existing research on CME analysis and compensation techniques. Based on the source of CME, this paper classifies CME into high-frequency and low-frequency components and discusses their causes and compensation methods, respectively. Additionally, the influence of different types of CME on other control strategies, such as sensorless and model predictive control, is discussed. The characteristics of CME compensation strategies for special current sensor installation positions are also explored. Finally, the paper summarizes the state of the art in CME analysis and compensation and discusses future trends in this field.