Responsive hydrogels that undergo controlled shape changes in response to a range of stimuli are of interest for microscale soft robotic and biomedical devices. However, these applications require fabrication methods capable of preparing complex, heterogeneous materials. Here we report a new approach for making patterned, multi-material and multi-responsive hydrogels, on a micrometre to millimetre scale. Nanolitre aqueous pre-gel droplets were connected through lipid bilayers in predetermined architectures and photopolymerized to yield continuous hydrogel structures. By using this droplet network technology to pattern domains containing temperature-responsive or non-responsive hydrogels, structures that undergo reversible curling were produced. Through patterning of gold nanoparticle-containing domains into the hydrogels, light-activated shape change was achieved, while domains bearing magnetic particles allowed movement of the structures in a magnetic field. To highlight our technique, we generated a multi-responsive hydrogel that, at one temperature, could be moved through a constriction under a magnetic field and, at a second temperature, could grip and transport a cargo.