Spontaneous chiral symmetry breaking is an ubiquitous phenomena characterizing very different physical systems in nature and it is central in condensed matter physics, elementary particle physics, and also in gravity. In this talk I will review my recent work on the subject. In particular, I will discuss how the background geometry itself can be viewed as an external condition and how it may affect the mechanism of spontaneous chiral breaking symmetry and, in turn, phase structure of an interacting fermion field theory.