Liposomes are well-known nanoparticles with a non-toxic nature and the ability to incorporate both hydrophilic and hydrophobic drugs simultaneously. As modern drug delivery formulations are produced by emerging technologies, numerous advantages of liposomal drug delivery systems over conventional liposomes or free drug treatment of cancer have been reported. Recently, liposome nanocarriers have exhibited high drug loading capacity, drug protection, improved bioavailability, enhanced intercellular delivery, and better therapeutic effect because of resounding success in targeting delivery. The site targeting of smart responsive liposomes, achieved through changes in their physicochemical and morphological properties, allows for the controlled release of active compounds under certain endogenous or exogenous stimuli. In that way, the multifunctional and stimuli-responsive nanocarriers for the drug delivery of cancer therapeutics enhance the efficacy of treatment prevention and fighting over metastases, while limiting the systemic side effects on healthy tissues and organs. Since liposomes constitute promising nanocarriers for site-targeted and controlled anticancer drug release, this review focuses on the recent progress of smart liposome achievements for anticancer drug delivery applications.