Perfect ideals of grade 3 can be classified based on algebra structures on their minimal free resolutions. The classification is incomplete in the sense that it remains open which of the possible algebra structures actually occur; this realizability question was formally posed by Avramov in 2012. Of five classes of algebra structures, the realizability question has been answered for one class. In this talk, we discuss and answer the realizability question for two classes and a partial answer for a third.