In the past decade, precise targeting through genome editing has emerged as a promising alternative to traditional therapeutic approaches. Genome editing can be performed using various platforms, where programmable DNA nucleases create permanent genetic changes at specific genomic locations due to their ability to recognize precise DNA sequences. Clinical application of this technology requires the delivery of the editing reagents to transplantable cells or to tissues and organs for approaches, often representing a barrier to achieving the desired editing efficiency and safety. In this review, authored by members of the GenE-HumDi European Cooperation in Science and Technology (COST) Action, we described the plethora of delivery systems available for genome-editing components, including viral and non-viral systems, highlighting their advantages, limitations, and potential application in a clinical setting.