In computational pathology, labels are typically available only at the whole slide image (WSI) or patient level, necessitating weakly supervised learning methods that aggregate patch-level features or predictions to produce WSI-level scores for clinically significant tasks such as cancer subtype classification or survival analysis. However, existing approaches lack a theoretically grounded framework to capture the holistic distributional differences between the patch sets within WSIs, limiting their ability to accurately and comprehensively model the underlying pathology. To address this limitation, we introduce HistoKernel, a novel WSI-level Maximum Mean Discrepancy (MMD) kernel designed to quantify distributional similarity between WSIs using their local feature representation. HistoKernel enables a wide range of applications, including classification, regression, retrieval, clustering, survival analysis, multimodal data integration, and visualization of large WSI datasets. Additionally, HistoKernel offers a novel perturbation-based method for patch-level explainability. Our analysis over large pan-cancer datasets shows that HistoKernel achieves performance that typically matches or exceeds existing state-of-the-art methods across diverse tasks, including WSI retrieval (n = 9324), drug sensitivity regression (n = 551), point mutation classification (n = 3419), and survival analysis (n = 2291). By pioneering the use of kernel-based methods for a diverse range of WSI-level predictive tasks, HistoKernel opens new avenues for computational pathology research especially in terms of rapid prototyping on large and complex computational pathology datasets. Code and interactive visualization are available at: https://histokernel.dcs.warwick.ac.uk/.