Plasma medicine is a new medical field with first very promising practical studies. However, basic research needs to be done to minimize risk and provide a scientific fundament for medical therapies. Therapeutic application of plasmas at or in the human body is a challenge both for medicine and plasma physics. Today, concepts of tailor-made plasma sources which meet the technical requirements of medical instrumentation are still less developed. To achieve selected effects and to avoid potential risks, it is necessary to know how to control composition and densities of reactive plasma components by external operation parameters. Therefore, a profound knowledge on plasma physics and chemistry must be contributed by physical research. Therapeutic applications required cold, non-thermal plasmas operating at atmospheric pressure. These plasmas are a huge challenge for plasma diagnostics, because usually they are small scale, constricted or filamentary, and transient. Regarding the manageability in everyday medical life, atmospheric pressure plasma jets (APPJ) and dielectric barrier discharges (DBD) are of special interest for medical applications. Working in open air atmospheres, complex plasma chemistry must be expected. Considering that, a great deal of effort combining experimental investigation and modelling is necessary to provide the required knowledge on plasma sources for therapeutic applications.