As a basic building block, optical resonant cavities (ORCs) are widely used in light manipulation. They can confine electromagnetic waves and improve the interaction between light and matter, which also plays an important role in cavity quantum electrodynamics, nonlinear optics and quantum optics. In recent years, the rise of metamaterials, artificial materials composed of subwavelength unit cells, has greatly enriched the design and functionality of ORCs. Here, we review zero-index hyperbolic metamaterials for constructing novel ORCs. First, this paper introduces the classification and implementation of zero-index hyperbolic metamaterials. Second, the distinctive properties of zero-index and hyperbolic cavities are summarized, including geometric invariance, homogeneous/inhomogeneous field distribution, topological protection (anomalous scaling law, size independence, continuum of higher-order modes, and dispersionless modes) for zero-index (hyperbolic) metacavities. Finally, the paper introduces some typical applications of zero-index and hyperbolic metacavities, and advances the research of metacavities.