Polyethylene is a model for semicrystalline polymers that provides the option to vary crystallinity within wide ranges and then to establish relationships between structure and mass and charge transport properties. Three different topics are covered: diffusion of n-hexane in polyethylene, extensive penetrant uptake kinetics, swelling and the design of a novel sensor, and finally electrical conduction in polyethylene, a field important to modern distribution of electric power (HVDC). This feature article presents past and ongoing studies at KTH Royal Institute of Technology using a variety of experimental methods and computer-aided simulation and modelling.