For many decades the measurement of body core temperature has been ubiquitously established in medical and non-medical applications, e.g., in hospitals, occupational medicine, sports medicine, military and other settings. However, there are still numerous challenges, such as the precise definition of the body core temperature, establishing the clinical importance of the measured temperature and the lack of a reliable, non-invasive and fast measurement method for body core temperature. After an introduction to the topic, the medical aspects from a user point of view are presented, i.e., the needs for temperature measurements, as well as possible measurement sites and clinical specifications and needs are highlighted. Subsequently, technical methods are presented which are used for temperature measurement. The analysis of the technical methods is divided into two sections: the first deals with the standard methods, which are currently used and the second describes methods, which are currently under development. Although temperature measurement appears very easy and is very common in daily use, it has many constraints, which are considered later. The need for further research is deduced from the above-mentioned sections and is finally followed by the conclusions section.