This thesis presents new geochronological, thermochronological, geochemical and isotopic data from igneous and meta-igneous rock samples from the Antarctic Peninsula during the Mesozoic. This crustal block, part of West Antarctica, has a long tectonic and magmatic history, complex topography and distinct geological provinces. Furthermore, the Antarctic Peninsula has been affected by complex convergent margin processes and defies simple classification as a convergent margin, magmatic arc or rifted continental margin. A new quantitative dataset is presented that includes analyses of (i) U-Pb zircon dates, (ii) zircon Lu-Hf isotopes, (iii) zircon O isotopes, (iv) Sr-Nd-Pb isotopes, (v) U-Pb apatite thermochronology and (vi) whole-rock geochemistry. This new dataset provides solid foundations for investigating the geological history of the Antarctic Peninsula and southwestern Gondwana, and they are used to construct a new model for the tectonic evolution of the margin of the Antarctic Peninsula and Patagonia during the late Palaeozoic and Mesozoic.