Liposomes and polymersomes are colloidal vesicles that are self-assembled from lipids and amphiphilic polymers, respectively. Because of their ability to encapsulate both hydrophilic and hydrophobic therapeutics, they are of great interest in drug delivery research. Today, the applications of liposomes and polymersomes have expanded to a wide variety of complex therapeutic molecules, including nucleic acids, proteins and enzymes. Thanks to their chemical versatility, they can be tailored to different drug delivery applications to achieve maximum therapeutic index. This review article evaluates liposomes and polymersomes from a perspective that takes into account the physical and biological barriers that reduce the efficiency of the drug delivery process. In this context, the design approaches of liposomes and polymersomes are discussed with representative examples in terms of their physicochemical properties (size, shape, charge, mechanical), targeting strategies (passive and active) and response to different stimuli (pH, redox, enzyme, temperature, light, magnetic field, ultrasound). Finally, the challenges limiting the transition from laboratory to practice, recent clinical developments, and future perspectives are addressed.