In this talk I will give a perspective on a class of discrete geometries motivated by causal set quantum gravity. In this approach the spacetime continuum is replaced by an ensemble of locally finite partially ordered sets obtained via a random, Poisson, process. These randomly generated discrete orders are meant to capture most of the topological and geometric information of the continuum spacetime, upto the discreteness scale: this is the fundamental conjecture of causal set theory. I will show using examples how the spacetime dimension, homology as well as several geometric invariants can be reconstructed from this discrete and highly "non-regular" substructure. I hope in the process to highlight the challenges involved and the new directions that are currently being explored in this quest for "geometry from order".