This thesis explores two complementary approaches to testing and understanding grav- ity beyond General Relativity (GR). The first part focuses on Generalized Proca theo- ries—vector-tensor models that extend the Proca action through derivative self-interactions and non-minimal couplings, while maintaining second-order equations of motion and avoid- ing ghost instabilities. We analyze the quantum consistency of these theories in both flat Minkowski spacetime and weakly curved backgrounds. In flat space, we compute one-loop corrections and observe the emergence of gauge-invariant structures, suggesting a form of radiative stability. In curved spacetime, we develop a scalar-vector-tensor (SVT) decom- position to isolate physical modes and consistently integrate out non-dynamical fields. Our results show that the theories remain well-behaved under quantum corrections, supporting their viability as effective field theories. The second part leverages gravitational wave (GW) observations as precision probes of strong-field gravity. Using convolutional neural networks (CNNs), we construct a ma- chine learning framework to classify GW signals as either consistent with GR or exhibiting beyond-GR (BGR) deviations. The dataset includes both artificial phase deformations and physically motivated waveforms derived using the parameterized post-Einsteinian (ppE) formalism. A key tool is the response function, which captures the sensitivity of the wave- form to small deformations. We show that training neural networks on response functions significantly improves classification accuracy and lowers detection thresholds. Applied to massive graviton models, this approach allows us to estimate the smallest graviton mass distinguishable from GR predictions. Together, these investigations form a coherent program to study modified gravity from both theoretical and observational perspectives, contributing to the broader effort of devel- oping consistent and testable alternatives to Einstein’s theory.