I describe the concept of a pulsar timing array and give broad overview of the construction of a pulsar timing array, methods for high-precision timing and noise characterization, and algorithms for gravitational wave detection and source characterization. I then provide an overview of worldwide pulsar timing programs and the scale and sensitivity of the pulsar timing array efforts, with particular attention to the International Pulsar Timing Array (IPTA). I discuss the most recent results from pulsar timing arrays, emphasizing the gravitational wave detection efforts in particular. Finally, I describe the anticipated future growth in participants, telescopes, pulsars, and sensitivity of the IPTA, highlighting the transformational advances that it will enable over the next decade.