Probabilistic graphical models are powerful frameworks that represent and reason through uncertainty in complex domains. The research addresses the challenges of representation, inference, and learning of PGMs within the settings of high-dimensional and incomplete data. We will be using both directed and undirected models in capturing these complex relationships between variables and make use of sophisticated inference techniques-for instance, belief propagation and Markov Chain Monte Carlo methods-to improve computational efficiency. Results of this paper prove that the integration of prior knowledge and the use of structured conditional probability distributions significantly improve model accuracy and robustness. We further apply PGMs to problems of medical diagnosis and image segmentation to portray their prowess in supporting informed decisions under uncertainty. The results indicate that, apart from helping in a better comprehension of complex systems by providing a versatile tool for knowledge discovery and predictive modelling, PGMs also support making informed decisions under uncertainty. Ultimately, the research offers continuous developments in PGMs, particularly insight into their practical applications and potentials for improvement in artificial intelligence and machine learning.