Pulsars are rapidly spinning neutron stars that act as incredibly precise celestial clocks, sending out pulses of radio waves at regular intervals. By carefully timing these pulses from many pulsars distributed across the sky, we can look for tiny modulations caused by passing gravitational waves—ripples in space-time predicted by Einstein. Gravitational waves are produced by some of the most dramatic events in the universe, such as pairs of supermassive black holes slowly spiraling together. A pulsar timing array synthesizes a Galaxy-sized gravitational wave detector by monitoring an ensemble of pulsars over decades. In this talk, I will explain how such a gravitational wave detector works, what we have recently discovered, and how they are opening a new window onto the universe. I will also briefly describe the work we are doing as part of the Indian Pulsar Timing Array experiment.