As a fundamental property of waves, diffraction plays an important role in many physical problems. However, diffraction makes waves in free space unable to be focused into an arbitrarily small space, setting a fundamental limit (the so-called diffraction limit) to applications such as imaging, lithography, optical recording and waveguiding, etc. Although the diffraction effect can be suppressed by increasing the refractive index of the surrounding medium in which the electromagnetic and optical waves propagate, such a technology is restricted by the fact that natural medium has a limited refractive index. In the past decades, surface plasmon polaritons (SPPs) have received special attention, owing to its ability to break through the diffraction limit by shrinking the effective wavelength in the form of collective excitation of free electrons. By combining the short wavelength property of SPPs and subwavelength structure in the two-dimensional space, many exotic optical effects, such as extraordinary light transmission and optical spin Hall effect have been discovered and utilized to realize functionalities that control the electromagnetic characteristics (amplitudes, phases, and polarizations etc.) on demand. Based on SPPs and artificial subwavelength structures, a new discipline called subwavelength electromagnetics emerged in recent years, thus opening a door for the next-generation integrated and miniaturized electromagnetic and optical devices and systems. In this paper, we review the theories and methods used to break through the diffraction limit by briefly introducing the history from the viewpoint of electromagnetic optics. It is shown that by constructing plasmonic metamaterials and metasurfaces on a subwavelength scale, one can realize the localized phase modulation and broadband dispersion engineering, which could surpass many limits of traditional theory and lay the basis of high-performance electromagnetic and optical functional devices. For instance, by constructing gradient phase on the metasurfaces, the traditional laws of reflection and refraction can be rewritten, while the electromagnetic and geometric shapes could be decoupled, both of which are essential for realizing the planar and conformal lenses and other functional devices. At the end of this paper, we discuss the future development trends of subwavelength electromagnetics. Based on the fact that different concepts, such as plasmonics, metamaterials and photonic crystals, are closely related to each other on a subwavelength scale, we think, the future advancements and even revolutions in subwavelength electromagnetics may rise from the in-depth intersection of physical, chemical and even biological areas. Additionally, we envision that the material genome initiative can be borrowed to promote the information exchange between different engineering and scientific teams and to enable the fast designing and implementing of subwavelength structured materials.