Chairperson, Graduate Committee: Neil J. CornishBecsy, BenceThis is a manuscript style paper that includes co-authored chapters.2023-01-272023-01-272022https://scholarworks.montana.edu/handle/1/17390Pulsar timing arrays monitor millisecond pulsars to detect gravitational waves with nanohertz frequencies. They provide valuable information about various astophysical processes inaccessible to electromagnetic observations. In particular, they could shed light on unsolved problems related to the formation and evolution of supermassive black holes. We present several new methods which will help us fully realize the detection potential of pulsar timing arrays. We explore how the large collection of supermassive black hole binaries in the Universe can appear as a stochastic gravitational wave background, and how it might also result in a few individually detectable binaries. We describe a new method to efficiently search for such individual binaries, and also how we can detect multiple binaries in the presence of the confusion noise from the stochastic background. Finally, we introduce a new approach to search for generic gravitational-wave bursts, which enables us to hunt for unexpected new types of sources on the nanohertz gravitational-wave sky.enPulsarsGravitational wavesBlack holes (Astronomy)DissertationCopyright 2022 by Bence Becsy