Accurate electrical load modeling is crucial for both transient and steady-state power system studies. Although various load modeling techniques are documented in the literature, a comprehensive review of the latest advancements in these techniques is lacking. This manuscript addresses this gap by presenting a detailed review of load modeling techniques, emphasizing their applications, recent advancements, and key distinguishing characteristics. Additionally, it explores the role of Digital Twin Models (DTM) in power systems, which offers a virtual representation of the system to simulate diverse operational scenarios and inform future investment and operational decisions. The integration of load models into DTMs poses challenges, such as computational demands and microcontroller limitations, which can be alleviated by adopting advanced load modeling techniques. This work further examines the application of load modeling techniques in the design and development of DTMs for power systems, as well as strategies to enhance the performance of load models in DTM applications. Finally, the manuscript outlines future research opportunities for integrating load modeling within DTM-based power system applications.