The ideal drug delivery system has a bioavailability comparable to parenteral dosage forms but is as convenient and easy to use for the patient as oral solid dosage forms. In recent years, there has been increased interest in transdermal drug delivery (TDD) as a non-invasive delivery approach that is generally regarded as being easy to administer to more vulnerable age groups, such as paediatric and geriatric patients, while avoiding certain bioavailability concerns that arise from oral drug delivery due to poor absorbability and metabolism concerns. However, despite its many merits, TDD remains restricted to a select few drugs. The physiology of the skin poses a barrier against the feasible delivery of many drugs, limiting its applicability to only those drugs that possess physicochemical properties allowing them to be successfully delivered transdermally. Several techniques have been developed to enhance the transdermal permeability of drugs. Both chemical (e.g., thermal and mechanical) and passive (vesicle, nanoparticle, nanoemulsion, solid dispersion, and nanocrystal) techniques have been investigated to enhance the permeability of drug substances across the skin. Furthermore, hybrid approaches combining chemical penetration enhancement technologies with physical technologies are being intensively researched to improve the skin permeation of drug substances. This review aims to summarize recent trends in TDD approaches and discuss the merits and drawbacks of the various chemical, physical, and hybrid approaches currently being investigated for improving drug permeability across the skin.