Large-N models, such as the SYK model and its variants provided useful zero dimensional toy models for studying strongly coupled fermion systems. In this talk, I will show that a certain class of these systems exhibits high Tc superconductivity entirely driven by repulsive interactions. Next, I will introduce a family of Gross-Neveu-Yukawa models that generalize the SYK models to translationally invariant systems in higher dimension. In one spatial dimension, we find a novel critical phase with neither fermonic nor bosonic quasiparticles. I will discuss the unique transport properties in this phase.