Over the past 15 years, the field of microrobotics has exploded with many research groups from around the globe contributing to numerous innovations that have led to exciting new capabilities and important applications, ranging from in vivo drug delivery, to intracellular biosensing, environmental remediation, and nanoscale fabrication. Smart responsive materials have had a profound impact on the field of microrobotics and have imparted small-scale robots with new functionalities and distinct capabilities. We have identified four large categories where the majority of future efforts must be allocated to push the frontiers of microrobots and where smart materials can have a major impact on such future advances. These four areas are the propulsion and biocompatibility of microrobots, the cooperation between individual units and human operators, and finally, the intelligence of microrobots. In this Review, we look critically at the latest developments in these four categories and discuss how smart materials contribute to the progress in the exciting field of microrobotics and will set the stage for the next generation of intelligent and programmable microrobots.