Over the past few decades, a range of vesicle-based drug delivery systems have entered clinical practice and several others are in various stages of clinical translation. While most of these vesicle constructs are lipid-based (liposomes), or polymer-based (polymersomes), recently new classes of vesicles have emerged that defy easy classification. Examples include assemblies with small molecule amphiphiles, biologically derived membranes, hybrid vesicles with two or more classes of amphiphiles, or more complex hierarchical structures such as vesicles incorporating gas bubbles or nanoparticulates in the lumen or membrane. In this review, we explore these recent advances and emerging trends at the edge and just beyond the research fields of conventional liposomes and polymersomes. A focus of this review is the distinct behaviors observed for these classes of vesicles when exposed to physical stimuli - such as ultrasound, heat, light and mechanical triggers - and we discuss the resulting potential for new types of drug delivery, with a special emphasis on current challenges and opportunities.