Charge density wave (CDW) order has been established as a generic feature of the cuprate phase diagram, competing and co-existing with superconductivity. While most commonly characterized by a translational symmetry breaking order parameter, CDW order can also involve a nematic order parameter. How these orders manifest and couple to each other can depend on the structure of the material and hole doping, and may play an important role in understanding differences in the cuprate phase diagrams of various materials. In this talk, we will show how we can use equilibrium and pump-probe resonant x-ray scattering measurements to measure both CDW order and nematic order in the (La,M)2CuO4 family of cuprate superconductors. These measurements demonstrate orbital/nematic order is coupled to but distinct from CDW order, existing above the CDW onset temperature in some samples. By measuring the nematic order as a function of doping, we show nematic order to be associated with the pseudogap phase of the cuprates, with signatures of nematic order present within the pseudogap phase, but vanishing above the pseudogap critical doping, p*, and temperature, T* in overdoped cuprates. We will also examine the role that structural symmetry plays in stabilizing CDW order. By applying uniaxial stress to modify the structure, we show that the CDW order is suppressed and superconductivity is enhanced.