Computational tools are ubiquitous in condensed matter physics, providing essential insights into many-body physics when analytical techniques fall short. This dissertation focuses on the application and interpretation of these tools, applied to the realm of frustrated systems, where competing interactions prevent the system from settling into simply ordered states. Frustrated systems often host exotic phenomena such as spin liquids, which make them an intriguing topic of study despite their inherent complexity. To tackle these challenges, a variety of computational techniques have been developed and refined over the years, such as density matrix renormalization group, quantum Monte Carlo, or projected entangled pair states. In the first part of this dissertation, we introduce a method to analyze improve variational numerical methods.Although recent developments in variational techniques have greatly expanded our ability to explore many-body Hilbert spaces, self-consistent evaluation of the quality of variational wavefunctions is a notoriously hard task. To tackle this, we propose a new way to evaluate variational ansatze using a method called Hamiltonian reconstruction by looking at the bias between original and reconstructed Hamiltonians. We apply the method to neural network wavefunctions for the J1-J2 model on a square lattice, which is a frustrated model long-standing open problem. From this method, we diagnose specific regions of poor performance of the variational ansatz and gain insight into specific directions for improvement. In the second part, we develop an approach for finding signatures of exotic and nonconventional phases by combining wavefunction snapshots with interpretable machine learning. Obtaining a ground state approximation of a Hamiltonian is only half the battle, since wavefunction amplitudes by themselves do not represent physically meaningful quantities. Thus, gaining insight into states can be just as formidable a task, especially when their true nature is unclear. We introduce a quantum-classical hybrid method of analyzing numerical results and apply it to a mysterious gapless phase of the honeycomb Kitaev model under external field. Using our method, we find that the machine learning procedure discovers features which we interpret as signatures and evidence of a spinon Fermi surface, guiding both theoretical and experimental searches for spin liquids. In the last part, we explore a new paradigm of frustration called orbital geometric frustration through the lens of twisted bilayer graphene. By introducing a new geometric framework for thinking about the extended flat-band Wannier states in twisted bilayer graphene, we connect the problem to the broader study of constrained plaquette models. From this framework arises the enticing possibility of fractional correlated insulating states with fractionalized quasiparticles, which we also approach with a numerical Monte Carlo study. Our investigations reveal a liquid state characterized by algebraic correlations with multi-flavored defects, a direct consequence of the unique form of frustration introduced by the extended Wannier orbitals' peculiar geometry. This finding not only enriches the theoretical framework of frustration in condensed matter physics but also opens up new avenues for experimental exploration in moire and flat-band materials.