Acoustofluidic technology enables the precise motion control of microfluids and their suspended matter through microscale flow channels or acoustic streaming mechanisms, featuring multi-functionality, high throughput, dynamic controllability, fast response, high precision, and low energy consumption. In recent years, numerous literatures have reviewed the development of acoustofluidic technology, discussing the acoustic manipulation modes of particles in microfluids and their applications. However, research on the surface acoustic wave-based acoustic manipulation of particles and fluids in different microfluids remains scarce. This paper aims to provide a comprehensive review of this topic, delving into the fundamental principles of surface acoustic wave-based acoustofluidic technology and discussing the latest advancements in this field. First, the basic theory of acoustofluidic technology is introduced along with the forces involved in manipulating particles and fluids, then the advantages and disadvantages of different types of surface acoustic wave devices are reviewed. Microfluids are categorized into two main types: Fluids within microchannels and droplets on open surfaces. The surface acoustic wave-based acoustic manipulation methods for their internal fluids and suspended particles are discussed separately. Subsequently, the advantages and limitations of surface acoustic wave-based platforms in the acoustic manipulation of fluids and particles are analyzed. The work concludes with a summary of the challenges faced by acoustic streaming in the field of fluid and particle manipulation, followed by prospects for the future development of acoustofluidic technology.