This topical overview is more particularly devoted to the low-temperature plasmas generated at atmospheric pressure that can potentially be used in both biomedical and plant biology applications. This underlines the interesting characteristics of such energetically and chemically nonequilibrium plasmas that involve many active species diluted in the background carrier gas (charged particles, radicals, atomic and molecular species, and ultraviolet radiations) and also plasma-induced electric fields. These gaseous active species are very interesting since they can efficiently irradiate many kinds of living biological tissue or surface because they can easily penetrate small pores, spread over rough surfaces, and reach, for instance, prokaryotic and eukaryotic cells. The main basic tools that are needed to experimentally and theoretically characterize such nonequilibrium plasmas are reviewed in order to identify and quantify the short-scale space and time evolution of the different plasma active species. Then, some relevant information is given on selected research works already done in the context of biomedical applications with a focus on some works done first on cancer cell inactivation to try to develop new therapies against cancer and second on cell membrane permeablization for gene transfection applications. Some biovegetal applications emphasizing interesting germination and plant growth stimulated by low-temperature plasma irradiation of different seeds are also evocated with their limits and expectations.