TlBr is relatively unique amongst semiconductors, in view of its very high density coupled with its large band-gap. In fact, its density (7.5 g cm-3) is comparable to bismuth germanate and thus it has excellent absorbing power for hard X- and gamma rays. For example, a 1 mm thick detector, has a usable efficiency of ~10% at 500 keV. Its lowest energy of operation is set by leakage currents at typically 1 keV. Such a wide dynamic range is ideally suited for a range of applications, such as gamma-ray astronomy, isotopic measurements for environmental redemption and particularly nuclear medicine, where small size and large stopping power are highly desirable attributes. Additionally, its band-gap energy of 2.7 eV is large enough to ensure low noise performance at room or even elevated temperatures. In this paper we assess the suitability of using TlBr arrays for X- and gamma-spectroscopy and specifically for nuclear medicine applications. For example, it is shown that the attributes of TlBr make it an ideal material for the production of intra-operative, radio-guided surgical probes, which operate in the hard X- and low energy gamma-ray regions. By using a segmented or pixelated anode design and tailoring the geometry to promote the near-field effect, most of the negative material attributes normally associated with TlBr (e.g. poor hole transport) can be largely negated.