Targeted drug delivery is proposed to reduce the toxic effects of conventional therapeutic methods. For that purpose, nanoparticles are loaded with drugs called nanocarriers and directed toward a specific site. However, biological barriers challenge the nanocarriers to convey the drug to the target site effectively. Different targeting strategies and nanoparticle designs are used to overcome these barriers. Ultrasound is a new, safe, and non-invasive drug targeting method, especially when combined with microbubbles. Microbubbles oscillate under the effect of the ultrasound, which increases the permeability of endothelium, hence, the drug uptake to the target site. Consequently, this new technique reduces the dose of the drug and avoids its side effects. This review aims to describe the biological barriers and the targeting types with the critical features of acoustically driven microbubbles focusing on biomedical applications. The theoretical part covers the historical developments in microbubble models for different conditions: microbubbles in an incompressible and compressible medium and bubbles encapsulated by a shell. The current state and the possible future directions are discussed.