Microbubble-assisted ultrasound has emerged as a promising method for the delivery of low-molecular-weight chemotherapeutic molecules, nucleic acids, therapeutic peptides, and antibodies in vitro and in vivo. Its clinical applications are under investigation for local delivery drug in oncology and neurology. However, the biophysical mechanisms supporting the acoustically mediated membrane permeabilization are not fully established. This review describes the present state of the investigations concerning the acoustically mediated stimuli (i.e., mechanical, chemical, and thermal stimuli) as well as the molecular and cellular actors (i.e., membrane pores and endocytosis) involved in the reversible membrane permeabilization process. The different hypotheses, which were proposed to give a biophysical description of the membrane permeabilization, are critically discussed.