Over the past decades, non-viral DNA and RNA delivery systems have been intensively studied as an alternative to viral vectors. Despite the most significant advantage over viruses, such as the lack of immunogenicity and cytotoxicity, the widespread use of non-viral carriers in clinical practice is still limited due to the insufficient efficacy associated with the difficulties of overcoming extracellular and intracellular barriers. Overcoming barriers by non-viral carriers is facilitated by their chemical structure, surface charge, as well as developed modifications. Currently, there are many different forms of non-viral carriers for various applications. This review aimed to summarize recent developments based on the essential requirements for non-viral carriers for gene therapy.