In her research, she develops novel hardware and software systems that advance personal fabrication technologies. Her work has been published at the premier venues for human-computer interaction (ACM CHI and ACM UIST) and has received several best paper and honorable mention awards. Mueller also serves on the ACM CHI and UIST program committees as an associate chair. In addition, she has been an invited speaker at universities and research labs such as MIT, Stanford, Berkeley, Harvard, CMU, Cornell, UW, ETH, Microsoft Research, Disney Research, and Adobe Research.