While gluons play a very fundamental role in quantum chromodynamics, their role in ordinary matter is not easily seen. However, theoretical predictions indicate that there should exist a family of particles to which the gluons explicitly contribute to the observable behavior (gluonic hadrons). The GlueX experiment at the Thomas Jefferson National Accelerator Facility is being built to find these new particles and map out their properties. Over the coming decade, experimental measurements are expected that will directly check these predictions and test our understanding of the role of gluons in ordinary matter.