Plasma medicine is an emerging application of low-temperature, atmospheric pressure plasmas to the treatment of several medical conditions. These plasmas are usually produced ionizing a noble gas flow with RF or pulsed high voltage. The presence in the flow of a fraction of air, or specific gases, causes the production of reactive chemical species which interact with the substrate to which the flow is applied. Metastable states of the noble gas also contribute to the interaction, through Penning ionization. The low power used in these plasma sources ensures that the flow remains at almost ambient temperature, so that no thermal effects are induced and living tissues can be treated in a harmless way. The most straightforward application is disinfection, thanks to the effect of the reactive species on the pathogens, especially bacteria, which lack the mechanisms of defense against oxidative stress which allow survival of the eukaryotic cells composing the substrate. Further applications rely on the ability of the activation of cellular processes, such as the intracellular generation of Reactive Oxygen Species (ROS), which can lead to therapeutic effects, including accelerated wound healing and cancer cell selective killing. In this contribution we present the advances made by our group in this field, showing experimental results concerning an indirect plasma treatment performed using a plasma source patented by our group. The targeted applications are the treatment of corneal infections (keratitis) and cancer treatment.