Frequency-selective structure (FSS) is a periodic artificial structure that can produce electromagnetic selectivity. Conventionally, it consists of single or multi-layer elements periodically arranged in a plane, which can manipulate spatial electromagnetic waves under different frequencies, polarizations, and angles of incidence. Various types of structures, analysis theories, and design methods have been developed for conventional FSSs. Unfortunately, these conventional surfaces manipulate electromagnetic waves through their 2-D or 2.5-D periodic elements, thus leading to serious limitations to their filtering performance and design flexibilities. Recently, a new class of 3-D FSS, consisting of 3-D multimode elements of waveguide cavities or transmission-line structures, has attracted much attention. Owing to this special construction of periodic elements, 3-D FSSs can provide more degrees of freedom in the spatial dimensions to exhibit superior performance features. This paper aims to provide a review of recent 3-D FSSs with a focus on the state-of-the-art techniques in the design and exploration of 3-D FSSs, as well as their promising applications in electromagnetic compatibility (EMC).