Successful drug development is a risky and lengthy process that can take over ten years and consume billions of dollars. Target discovery is a critical stage of drug development for the identification of key molecules and pathways that can be targeted by novel therapeutics to find more effective treatments. Due to the rapid development in artificial intelligence and machine learning techniques over the past decade, computational approaches have now emerged as powerful tools to unravel complex interactions within biological systems to identify novel therapeutic targets. In particular, modeling and analysis of intracellular molecular networks play a pivotal role in target discovery by enabling researchers to efficiently and simultaneously navigate massive amounts of biological data to identify potential therapeutic targets. Such technologies can significantly accelerate the prolonged process of development of innovative therapies for complex diseases. Besides highlighting the findings of the recently introduced extreme signaling failures in intracellular molecular networks, here we briefly review various methods for modeling and analysis of intracellular molecular networks and discuss how they can be utilized to predict potential drug targets within such complex signaling systems. Overall, this review emphasizes the significance of modeling and analysis of molecular networks for fast-tracking and rapid discovery of novel therapeutic targets; to pave the way for the development of more effective treatments.