Nucleic acid based drugs (NADBs) are short DNA/RNA molecules that include among others, antisense oligonucleotides, aptamers, small interfering RNAs and micro-interfering RNAs. Despite the different mechanisms of actions, NABDs have the ability to combat the effects of pathological gene expression in many experimental systems. Thus, nowadays, NABDs are considered to have a great therapeutic potential, possibly superior to that of available drugs. Unfortunately, however, the lack of effective delivery systems limits the practical use of NABDs. Due to their hydrophilic nature, NABDs cannot efficiently cross cellular membrane; in addition, they are subjected to fast degradation by cellular and extracellular nucleases. Together these aspects make the delivery of NABDs as naked molecules almost un-effective. To optimize NABD delivery, several solutions have been investigated. From the first attempts described in the beginning of the 1980s, a burst in the number of published papers occurred in the beginning of 1990s reaching a peak in 2012-13. The extensive amount of work performed so far clearly witnesses the interest of the scientific community in this topic. In the present review, we will concentrate on the description of the most interesting advances in the field. Particular emphasis will be put on polymeric and lipid materials used alone or in combination with a promising delivery strategy based on the use of carbon nanotubes. The data presented suggest that, although further improvements are required, we are not far from the identification of effective delivery systems for NABDs thus making the clinical use of these molecules closer to reality.