Cross-platform heterogeneity creates a persistent domain-shift problem: the same real-world event is described differently across platforms due to distinct content formats, user norms, modality mixes, and temporal dynamics. This chapter presents Self-Supervised Modality Complementation (SSMC), a framework that reduces reliance on platform-specific labels while explicitly handling missing modalities. We first analyze the coupled challenge of heterogeneity and incompleteness and explain why naive platform-invariant training can fail under modality mismatch. We then introduce SSMC with two core components: a Missing Data Complementation module to regularize and impute absent modality cues, and a Multimodal Self-Learning module that aligns representations through self-supervised objectives for cross-platform transfer. Next, we present the Cross-Platform Social Event Detection (CSED) dataset and describe its design goals and curation pipeline to evaluate robustness under realistic platform shifts. Finally, experimental results demonstrate improved transferability, missing-modality resilience, and stability under distribution changes, and we discuss failure modes and practical recommendations for cross-platform monitoring systems.