Irregular spatiotemporal data, characterized by collections of asynchronous observations at different time instants and spatial coordinates, pose a complex challenge in data analysis. These structured data are commonly encountered in sensor networks, such as environmental monitoring networks, traffic management systems, and social media analytics. Unlike their regular counterparts, the inherent irregularities in the data make it difficult for the processing methods to exploit the underlying temporal and spatial structures. Yet, the ability to effectively analyze and model such data is crucial for making informed decisions in domains where understanding complex dynamics is of paramount importance. The objective of my doctoral research is to develop methodologies for predictive problems on irregular spatiotemporal data by exploiting graph-based representations. Graphs, indeed, provide a natural way to capture the relational information associated with spatial irregularities, such as the distance between sensors or the correlations among signals. In particular, my research focuses on three fundamental problems, namely, imputation, regularization, and prediction. Imputation techniques are explored to reconstruct missing data by leveraging valid observations and neighboring nodes in the graph. Regularization methods are developed to filter out noise by enforcing spatiotemporal consistency. Finally, forecasting methodologies are investigated, to predict future observations by taking advantage of spatiotemporal dependencies.