Cold plasma (CP) is an ionised gas containing excited molecules and ions, radicals, and free electrons, and which emits electric fields and UV radiation. CP is potently antimicrobial, and can be applied safely to biological tissue, birthing the field of plasma medicine. Reactive oxygen and nitrogen species (RONS) produced by CP affect biological processes directly or indirectly via the modification of cellular lipids, proteins, DNA, and intracellular signalling pathways. CP can be applied at lower levels for oxidative eustress to activate cell proliferation, motility, migration, and antioxidant production in normal cells, mainly potentiated by the unfolded protein response, the nuclear factor-erythroid factor 2-related factor 2 (Nrf2)-activated antioxidant response element, and the phosphoinositide 3-kinase/protein kinase B (PI3K/Akt) pathway, which also activates nuclear factor-kappa B (NFκB). At higher CP exposures, inactivation, apoptosis, and autophagy of malignant cells can occur via the degradation of the PI3K/Akt and mitogen-activated protein kinase (MAPK)-dependent and -independent activation of the master tumour suppressor p53, leading to caspase-mediated cell death. These opposing responses validate a hormesis approach to plasma medicine. Clinical applications of CP are becoming increasingly realised in wound healing, while clinical effectiveness in tumours is currently coming to light. This review will outline advances in plasma medicine and compare the main redox and intracellular signalling responses to CP in wound healing and cancer.