The drug discovery process is challenging, time-consuming, and costly, with drug target identification being an essential step in developing effective therapies. Drug repurposing offers a strategy for identifying new uses for existing drugs, aiming to simplify the process. Machine learning models and network analysis methods have demonstrated promise in both drug target identification and repurposing, providing powerful tools for analyzing complex biological data. This thesis will explore the applications of neural networks and multilayer biological networks for drug repurposing opportunities and network inference problems applied to signaling pathways. A novel machine learning and network-based workflow is presented for identifying drug targets for cystinosis, a rare disease that causes progressive kidney disease, currently lacking effective therapies to prevent the kidney failure. This approach permits to recapitulate the disease mechanisms in the context of renal tubular physiology and identify candidate drug targets for further validation using a cross-species workflow and disease-relevant screening technologies. While machine learning approaches have shown promise, they often need more mechanistic understanding, which is necessary for robust drug target identification and repurposing strategies. Mechanistic models provide crucial insights into the underlying biological mechanisms, complementing machine learning techniques. However, inferring mechanistic signaling networks from omics data poses challenges due to non-identifiability, resulting in multiple valid solutions consistent with the data. After that, the focus shifts towards quantifying signaling model diversity through solver-agnostic solution sampling with CORNETO, an ongoing effort that aims to unify network inference problems via constrained optimization. Mechanistic signaling networks can be inferred from omics data and prior knowledge using combinatorial optimization and mathematical solvers to find the optimal network. However, this problem is in general, non-identifiable, and several solutions may be equally valid. Ignoring the existence of these alternative solutions leads to an incomplete picture of the hypothesis space of consistent mechanistic signaling networks. To alleviate this issue, an algorithm to explore the space of alternative solutions and to conduct sensitivity analysis on the optimal solution is implemented and presented. These algorithms are applied to data from pancreatic cancer cell lines treated with kinase inhibitors to study cellular responses to drug perturbations by inferring mechanistic signaling networks from omics data.