Acoustofluidics offers contact-free manipulation of particles and fluids, enabling their uses in various life sciences, such as for biological and medical applications. Recently, there have been extensive studies on acoustic streaming-based acoustofluidics, which are formed inside a liquid agitated by leaky surface acoustic waves (SAWs) through applying radio frequency signals to interdigital transducers (IDTs) on a piezoelectric substrate. This paper aims to describe acoustic streaming-based acoustofluidics and provide readers with an unbiased perspective to determine which IDT structural designs and techniques are most suitable for their research. This review, first, qualitatively and quantitatively introduces underlying physics of acoustic streaming. Then, it comprehensively discusses the fundamental designs of IDT technology for generating various types of acoustic streaming phenomena. Acoustic streaming-related methodologies and the corresponding biomedical applications are highlighted and discussed, according to either standing surface acoustic waves or traveling surface acoustic waves generated, and also sessile droplets or continuous fluids used. Traveling SAW-based acoustofluidics generate various physical phenomena including mixing, concentration, rotation, pumping, jetting, nebulization/atomization, and droplet generation, as well as mixing and concentration of liquid in a channel/chamber. Standing SAWs induce streaming for digital and continuous acoustofluidics, which can be used for mixing, sorting, and trapping in a channel/chamber. Key challenges, future developments, and directions for acoustic streaming-based acoustofluidics are finally discussed.