Two-dimensional (2D) transition metal dichalcogenides (TMDCs) are promising candidates for a plethora of applications from (opto)electronics and sensors to DNA sequencing and catalysis. The investigation of radiation effects in these materials is often underpinned by one or more of the following motivations. Firstly, elucidation of the fundamental radiation-nanostructure interactions that govern defect production in 2D crystals and how these compare to the relatively well-understood radiation damage mechanisms of bulk materials. Secondly, engineering the electronic, optical and catalytic properties of 2D TMDCs via controlled defect formation under ionising radiation with a view to improving device performance and enabling new applications. Thirdly, irradiation of 2D TMDC devices using ion accelerators/gamma sources to emulate specific radiation fields and environments in order to elucidate the suitability of these materials for detection or radiation-hard applications. The experimental work presented in this thesis is closely aligned with these motivations and describes: (I) The influence of crystal thickness on the radiation damage mechanisms in 2D MoS2 as a function of radiation type. Changes in the crystallinity, optical properties, chemical composition, vibrational properties and morphology of gamma and heavy ion-irradiated crystals are systematically studied using various spectroscopic and microscopic techniques. (II) The efficacy of heavy ion-mediated defect-engineering in modulating the electronic properties of 2D MoS2 crystals deposited on widely used SiO2/Si substrates. Through a careful consideration of ion mass and kinetic energy, nuclear energy transfer mechanisms are promoted and lead to p-doping of MoS2 via vacancy production and charge transfer interactions. (III) The impact of production method on the radiation damage mechanisms in TMDCs under gamma and ion irradiation. This is achieved by utilising single crystals, solution processed nanosheets and single layer polycrystalline films, produced by micromechanical exfoliation, liquid phase exfoliation and chemical vapour deposition, respectively. (IV) The stability of 2D MoS2 crystals under gamma irradiation within the absorbed dose regime relevant for nuclear industry applications. The observation of etching, doping and oxidation will inform the suitability of this material for radiation-hard applications.