In this paper, we demonstrate two studies where fused-deposition modelling (FDM) is used to fabricate composites with (1) controlled hyperelastic property gradients and (2) shape-memory behaviour. In the first study, we first fabricate thermoplastic elastomer scaffolds consisting of freely suspending fibers through FDM and then encapsulate them with soft silicone elastomers. We first present our studies on how the scaffold geometry is correlated with the printing speed and flow rate. Next, through tensile testing, we demonstrate the capability of the method in generating structures with (1) different hyperelastic properties through scaffold design and printing parameter control and (2) controlled spatial gradients of such properties. In the second study, we use multi-material FDM to manufacture composite structures consisting of a thermoplastic elastomer shell and polycaprolactone (PCL) core. Owing to the lower melting point and higher room temperature modulus of the PCL, these composites exhibit shape memory behaviour if subjected to thermal cycling between the room temperature and the melting point of the PCL. We evaluate the geometry and temperature dependence of this behaviour. We also demonstrate the reprogrammability of the memorized shape by introducing a silicone encapsulation for the composites.