Interatomic potentials are essential for driving molecular dynamics (MD) simulations, directly impacting the reliability of predictions regarding the physical and chemical properties of materials. In recent years, machine-learned potentials (MLPs), trained against first-principles calculations, have become a new paradigm in materials modeling as they provide a desirable balance between accuracy and computational cost. The neuroevolution potential (NEP) approach, implemented in the open-source GPUMD software, has emerged as a promising machine-learned potential, exhibiting impressive accuracy and exceptional computational efficiency. This review provides a comprehensive discussion on the methodological and practical aspects of the NEP approach, along with a detailed comparison with other representative state-of-the-art MLP approaches in terms of training accuracy, property prediction, and computational efficiency. We also demonstrate the application of the NEP approach to perform accurate and efficient MD simulations, addressing complex challenges that traditional force fields typically can not tackle. Key examples include structural properties of liquid and amorphous materials, chemical order in complex alloy systems, phase transitions, surface reconstruction, material growth, primary radiation damage, fracture in two-dimensional materials, nanoscale tribology, and mechanical behavior of compositionally complex alloys under various mechanical loadings. This review concludes with a summary and perspectives on future extensions to further advance this rapidly evolving field.