Ultrafast electron microscopy (UEM), also referred to as four-dimensional electron microscopy (4D-EM), has emerged as a transformative tool capable of recording atomic-scale dynamics with high spatiotemporal resolution. While the stroboscopic pump–probe mode has been extensively applied to reversible processes, many important phenomena are intrinsically irreversible and demand single-shot imaging. This review focuses on the principles and recent progress of single-shot 4D-EM for capturing non-repeatable events in space and time. We describe the two main single-shot modalities — single-frame and movie-mode (multi-frame) imaging — which rely on intense, ultrashort electron pulses to capture a transient following a single pump excitation. Representative applications are systematically surveyed, including laser-induced melting and rapid solidification, phase transitions, nanoparticle jumping and coalescence, redox and eutectic reaction dynamics, and liquid-phase behaviors. Key challenges, including the conflict between electron number and pulse duration imposed by space-charge effects, beam coherence, and detector limitations, are discussed, where correspondingly future perspectives and strategies are offered. The progress establishes single-shot 4D-EM as an indispensable platform for unraveling irreversible and stochastic processes across materials science, chemistry, physics, and biology.

Non-Hermitian physics provides a powerful route for controlling wave propagation in open systems, yet its role in spatially inhomogeneous topological structures remains insufficiently clarified. Here, we experimentally demonstrate a spatially inhomogeneous non-Hermitian topological metasurface on a microwave microstrip platform. A continuous geometric modulation introduces a position-dependent Dirac mass and forms a mass-domain-wall interface, while lumped resistive loading provides a controllable imaginary potential. This design transforms the conventional Hermitian degeneracy into a real-part degenerate region near the Γ point, accompanied by an imaginary-frequency bifurcation and mode-dependent attenuation. Tight-binding calculations, full-wave simulations, and microwave near-field measurements are used to characterize the complex bulk dispersion and lossy edge-state transport. We further show that the edge modes exhibit pseudospin-momentum-locked directional excitation, with non-Hermiticity providing an additional degree of freedom for attenuation and mode selectivity. These results clarify the distinct roles of geometric mass gradients and engineered dissipation, establishing a tunable microwave platform for loss-engineered topological wave transport.