Since the beginning of metamaterial research, epsilon-near-zero metamaterials have long been a research hotspot in the field of electromagnetic metamaterials because of the electromagnetic features granted by their near-zero effective permittivity, making them interesting in both theoretical studies and technical applications. To achieve the near-zero effective permittivity response, in short, the current epsilon-near-zero metamaterial research follows three fundamental theories, the waveguide theory, the band structure theory for photonic crystals, and the effective medium theory. In general, the waveguide theory makes the epsilon-near-zero metamaterials operate as a waveguide at the cut-off frequency, while the band structure theory makes the epsilon-near-zero metamaterials perform as a photonic crystal at the frequency of the Dirac point. On the other hand, the effective medium theory follows another principle of the cancellation of the positive permittivity and the negative permittivity of different components of the epsilon-near-zero metamaterials at a specific frequency. All three theories strongly depend on the electromagnetic properties and the microstructures of the components in the epsilon-near-zero metamaterials, which also limits the near-zero permittivity response frequency. In brief, the single operating frequency and operating mode caused by the inherent limitation of these theories is always a bottleneck preventing further applications of the epsilon-near-zero metamaterials. Therefore, how to break through the limitations, to realize the broadband near-zero permittivity response of metamaterials under multi-stimulation modes, to master its physical principles, and to establish a new theoretical framework are of great significance in theoretical research and application development.In this work, we present a systematic review of our research on broadband epsilon-near-zero metamaterials to address the single operating frequency issue of current epsilon-near-zero metamaterials. In our research, we establish a spectral representation theory for the broadband epsilon-near-zero metamaterials based on the Bergman-Milton spectral representation theory of effective medium theory concerning the characteristics of the effective permittivity spectral representation of typical microstructures of metamaterials and theoretically demonstrate the application of the spectral representation theory in various broadband epsilon-near-zero metamaterials construction. To be specific, the spectral representation theory for the broadband epsilon-near-zero metamaterials firstly abstracts the material and the microstructural properties of the metamaterials into a simple algebra model, in which the broadband near-zero permittivity response can be constructed as will for different probing electromagnetic waves. After that, the spectral representation theory exactly maps the spectral representation of the broadband epsilon-near-zero metamaterials into the physical structures via an analytical inverse algorithm. Through the spectral representation theory, we successfully realize broadband epsilon-near-zero metamaterials with different superlattice configurations in theory, such as the multilayer and the Hashin-Shtrikman structures. Meanwhile, we clearly explain the physical principles of the broadband near-zero permittivity response by numerical simulations. The broadband epsilon-near-zero metamaterials successfully extend the near-zero permittivity property into a wide operating frequency band without changing the near-zero permittivity property. Therefore, they expand the application potential of the epsilon-near-zero metamaterials in broadband optical field manipulation. Through the numerical simulation, we demonstrate several applications of the designed broadband epsilon-near-zero metamaterials, such as the broadband electromagnetic tunneling and focusing, the broadband electromagnetic wave directional emission, and the broadband electromagnetic wavefront modulation. In the end, we wish our achievement can enrich the fundamental theory and application prospects of electromagnetic metamaterials.