Simultaneous electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) provide complementary views of brain activity, capturing neural dynamics across temporal and spatial scales. Integrating these modalities offers a powerful approach for studying brain function, yet remains fundamentally challenging due to differences in measurement mechanisms, temporal resolution, and neurovascular coupling. At its core, EEG–fMRI fusion can be viewed as an inverse problem: the goal is to recover latent neural processes that are only partially observed through electrophysiological and hemodynamic signals. Here, we review data-driven fusion methods developed between 2000 and 2025, focusing on approaches that aim to identify shared neural representations across modalities. We organize the existing methods according to the fusion strategy (symmetric vs. asymmetric), the methodological objective (factorization vs. translation), and the modeling assumptions (linear vs. non-linear), and discuss commonly-used evaluation metrics and visualization strategies. We further examine evaluation strategies, highlighting the lack of a universal validation standard and the challenges of interpreting latent multimodal components. Across neurological, psychiatric, and cognitive applications, EEG-fMRI fusion has revealed distributed network dynamics that are not accessible through unimodal analyses. However, key challenges remain, including temporal misalignment, noise-induced coupling, and model-dependent interpretation. We discuss emerging directions such as nonlinear modeling, flexible coupling frameworks, and large-scale group-level fusion, which may enable more robust and interpretable multimodal integration. Together, this review reframes EEG-fMRI fusion as a problem of latent neural inference and outlines a path toward more principled, scalable, and biologically grounded approaches for understanding brain function and dysfunction.