Neutrinos are the most elusive particles known to humanity, and their nature has puzzled physicists for decades. While great strides in understanding neutrinos have been made in the past three decades, many open questions about them remain, including their absolute mass scale, the nature of their masses, and the extent to which they violate \textsf{CP} symmetry. The fact that neutrinos are indeed massive has shown that the Standard Model of particle physics, while wildly successful, is incomplete. This fact has motivated searches for Beyond Standard Model processes that may fundamentally change our understanding of nature. Among these potential processes is neutrinoless double beta decay $(0\nu\beta\beta)$, a theorized lepton number violating process. Experimental evidence of $0\nu\beta\beta$ decay would conclusively show that neutrinos are Majorana fermions. This has profound implications for particle physics, as it would help to explain the matter-antimatter asymmetry in the universe while also providing insight into the origins of the masses of neutrinos.

The Cryogenic Underground Observatory for Rare Events (CUORE) experiment is an ongoing experiment searching for $0\nu\beta\beta$ decay in $^{130}$Te. This dissertation outlines the current status of the ongoing global search for $0\nu\beta\beta$ and details how the CUORE experiment is contributing to this effort. The results presented here showcase the use of a novel noise cancellation algorithm to improve the CUORE data quality, including the RMS noise, energy resolution, and threshold. The application of this algorithm to CUORE's latest dataset with 2039 kg-years of TeO$_2$ exposure is then detailed. The results from CUORE's search for $0\nu\beta\beta$ decay using this dataset are also reported. No evidence for $0\nu\beta\beta$ decay is found, and an upper limit on the decay rate of $\Gamma_{0\nu} < 2.0 \times 10^{-26}$ yr$^{-1}$ (90\% C.I.) is placed, corresponding to a lower limit on the half-life of $T_{1/2}^{0\nu} > 3.5 \times 10^{25}$ yr. The 90\% C.I. exclusion sensitivity to $0\nu\beta\beta$ decay is $T_{1/2}^{0\nu} = 4.4 \times 10^{25}$ yr, and the $3\sigma$ discovery sensitivity is $T_{1/2}^{0\nu} = 2.6 \times 10^{25}$ yr. Finally, future searches for $0\nu\beta\beta$ decay beyond CUORE and the prospects of noise decorrelation algorithms for these searches are discussed.