Cold plasma (CP) is an ionised gas containing excited molecules and ions, radicals, free electrons, and 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, Nrf2-activated antioxidant response element and PI3K/Akt pathway, which also activates NFκB. At higher CP exposures, inactivation, apoptosis and autophagy of malignant cells can occur via degradation of PI3K/Akt and 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.