This talk presents recent advances on online matching under budget constraints and community structure, based on two works: Dynamic Online Matching with Budget Refills [1] and Online Matching on Stochastic Block Model [2]. Online matching provides a natural framework for studying how digital platforms allocate resources in real time, in applications such as organ exchange, appointment scheduling, and ride-sharing. Online advertising serves as the central motivation for these projects: in this setting, users and advertisers are matched sequentially under budget constraints and heterogeneous interaction patterns, making it a particularly rich and practically significant environment for analyzing adaptive decision-making under uncertainty. From a theoretical perspective, the presentation lies at the intersection of online matching and multi-armed bandit theory, combining the combinatorial and sequential structure of allocation with the exploration–exploitation trade-off that arises when system parameters are unknown. The first part studies online matching with budget refills, motivated by platforms in which advertisers’ budgets are periodically replenished, and establishes performance guarantees in both adversarial and stochastic environments, highlighting how refill frequency and structure influence algorithmic competitiveness. The second part investigates online matching in structured environments modeled by a Stochastic Block Model, capturing community structure among users and advertisers; when compatibility probabilities between communities are unknown, the problem becomes a structured bandit setting, and algorithmic approaches that combine exploration with balanced allocation are analyzed together with theoretical guarantees on convergence and expected matching performance.