Deep generative models have made rapid progress in image, text, audio, and video generation, and are increasingly being applied to structured records. For tabular data, however, generative modeling remains difficult: a dataset may contain numerical and categorical attributes, missing values, sensitive fields, imbalanced categories, complex feature dependencies, and domain constraints. Earlier tabular data modeling methods based on GANs or VAEs have achieved useful results, but they can suffer from unstable training, mode collapse, weak modeling of multimodal distributions, and fragile handling of mixed-type features. Diffusion models have therefore attracted growing interest because their noising-and-denoising formulation provides a flexible and stable way to model complex data distributions, and has been adapted to tabular synthesis, missing-value imputation, trustworthy data generation, and anomaly detection. Flow matching offers a closely related route by learning transport vector fields along probability paths, often with more direct control over path design and sampling efficiency. Despite this progress, the literature on diffusion and flow matching models for tabular data remains difficult to compare because methods target different tasks and rely on different representations, objectives, evaluation protocols, and domain assumptions. To the best of our knowledge, this is the first survey dedicated specifically to diffusion and flow matching models for tabular data. We review work from June 2015 to May 2026, organize it around data-engineering challenges, tasks, design choices, and evaluation dimensions, and discuss open problems in scalability, feature dependency modeling, privacy, fairness, benchmarking, and constraint-aware generation. We maintain updates in a GitHub repository.