This work investigates whether thermal histories of rocks can be reliably reconstructed by interpreting step-heating 40Ar/39Ar analyses of alkali feldspar via multi-diffusion domain (MDD) theory. It includes three chapters addressing the validity of the key assumptions of MDD theory, which are that each alkali feldspar grain contains multiple stable intra-grain diffusion domains and that these domains lose 40Ar by diffusion. The first chapter presents numerical modelling results that were used to evaluate some of the arguments supporting the use of MDD theory. The second chapter presents step-heating 40Ar/39Ar analyses of alkali feldspar and experimental data on microtextural evolution of alkali feldspar during step-heating that were used to identify intra-grain diffusion domains and assess their stability. The third chapter presents in situ 40Ar/39Ar analyses of alkali feldspar and petrological data that were used to identify the mechanism of 40Ar loss. The data presented here allow to advise against using MDD theory.