Abstract: Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and one encounters the problem of recovering the matrix given only incomplete and indirect observations. The last decade has seen tremendous advances in both the theory and algorithms for this setting. In this talk I will discuss challenging versions of the low-rank matrix recovery problem in settings where our observations are highly quantized or consist of event counts, describing both existing results as well as open problems in this space.