The superconducting copper oxides might appear interesting because of high-temperature superconductivity, but their real beauty is in the complex quantum phase space that a small set of interactions yields. Understanding these phases and their connection is among the key intellectual challenges of our time. In this talk, we discuss the phase of 2-dimensional charge order and its connection with superconductivity. First, we survey some of our latest results pertaining to the in-plane structure of the charge order, which is more intriguing than originally thought. Second, we will show a new way to produce 3-dimensional charge order by engineering the orbital character of the CuO2 wavefunction, which can offer a new way of studying the validity of single-band models used to describe 2-dimensional systems.