Small particles of gold (< 100 nm) have attracted great interest among researchers due to the unique combination of their physicochemical properties. Among various research areas catalysis and bio-nanotechnology represent the largest areas of growth for gold nanoparticle research. Catalysts play a crucial role in the life of the modern society. More than 85 % of all chemical processes are catalytic, and this number is increasing every year. There is a constant demand to develop more efficient and durable catalysts in order to address increasing energy demands and environmental requirements. The first part of the thesis is focused on the study of catalytic activity of supported gold and mixed-metal catalysts, derived from atomically precise phosphine-stabilised gold and mixed-metal clusters in the liquid-phase oxidation of cyclohexene and one-pot synthesis of imines. Various characterisation techniques (TEM, diffuse-reflectance UV-vis, XPS, etc.) as well as kinetic studies were used in order to establish the optimal structure of gold catalysts. The effect of catalytic support, nature of hetero-metal atom for mixed metal-systems and type of catalyst pre-treatment were also examined. Gold nanoparticles are actively studied in various biomedical applications as they are offering new approaches to the detection and treatment of life-threatening diseases, such as cancer. The second part of this work discusses our preliminary investigations of biological activity of gold nanoparticles, stabilised with cancer-targeting molecules. In particular, the cytotoxicity of gold nanoparticles was studied using 11 different cancer and normal cell types. Gold uptake and particle localisation inside the cells were also investigated.