Pulsar timing measurements are influenced by gravitational waves (GW) along the line of sight from Earth to the pulsar. Combining timing measurements of many sources forms a GW detector that is sensitive to the nanohertz region of the GW spectrum. Current GW limits from pulsar timing are within an order of magnitude of the predicted strength of the stochastic GW background created by binary massive black hole systems. This has recently created renewed interest in the topic, and several research groups around the world are conducting timing programs designed to detect GW. I will review the state of our current observations, and describe the experimental challenges faced in moving to the next level. These include ongoing efforts in instrumentation, data analysis, and pulsar searching, as well as increasing our understanding of unavoidable systematic effects (due to the interstellar medium and intrinsic neutron star processes) that may ultimately limit any pulsar timing GW detection.