Spectral imaging (SI) is a technique that combines spatial imaging and spectroscopy to acquire a three-dimensional (3D) spatio-spectral datacube. Due to its ability to capture abundant spectral information at each spatial location, SI has been rapidly developed and widely used in various fields. Traditional SI methods resolve spatio-spectral information through various scanning techniques, including spectral scanning and spatial scanning, which provide either high spectral or high spatial resolution. However, scanning strategy increases the systematic complexity and reduces the detection efficiency, which hinder the applications in agriculture, aviation, military, civil and other fields. In contrast, computational spectral imaging systems have garnered increasing attention in recent years due to their compact and simplified design, high throughput, and reduced size. Moreover, computational spectral imaging systems based on broadband spectral modulation, are more easily integrated and capable of achieving higher spectral resolution. Consequently, computational spectral imaging based on broadband spectral modulation holds significant potential to achieve high spatial-spectral resolution, miniaturization, single-exposure operation, and high luminous flux. As a result, it has emerged as a prominent research focus in the field of spectral imaging in recent years. First, the fundamental principles of computational imaging based on broadband spectral modulation are introduced, including the theory of compressed sensing, the mechanism of spectral modulation, and spectral reconstruction algorithms. In broadband spectral modulation-based computational spectral imaging, the spectrum of an object is modulated using broadband response materials, and the signal is captured by a detector without spectral resolution. According to compressed sensing theory, the number of samples required for signal reconstruction can be significantly smaller than the number of spectral channels. However, the spectral response curve of the materials must exhibit sufficient randomness. This is because, within the compressed sensing framework, the sensing matrix must have low correlation to efficiently sample the signal of objects. Since the spectral response curve of materials cannot be arbitrarily designed, enhancing its randomness becomes a critical area of research for computational spectral imaging systems based on spectral response. Conventional spectral response materials include nanomaterials (e.g., quantum dots, photonic crystals, metasurfaces, and nanowires), Fabry-Perot (F-P) cavities, liquid crystals, optical films, and composite materials. The principles of spectral modulation vary across these materials. For example, quantum dot materials can shift the spectral response by adjusting their size. Photonic crystals and metasurfaces achieve spectral modulation by altering their microstructures. Fabry-Perot (F-P) cavities modulate the spectral response by changing the cavity length or the refractive index of the material inside the cavity. Liquid crystal filters control the effective refractive index by varying the applied voltage, which induces different phase delays for different wavelengths, resulting in wavelength-dependent intensity attenuation and modulation of the spectrum. Optical thin films enable spectral modulation by controlling the number of layers, the refractive index, and the thickness of the filter layers. Although various spectral response curves can be generated, their shapes cannot be arbitrarily controlled. As a result, researchers typically design a mass of broadband spectral response curves and then select those with the lowest correlation based on correlation analysis. The result-oriented reverse design method allows for the selection of a target spectral curve from a set of potential curves. This method reduces the sensitivity of the spectral curve to angle variations and noise during the optimization process and can even enable the design of arbitrary spectral curves. Consequently, this approach has become a key technique in spectral response imaging. Furthermore, Spectral modulation materials have certain limitations. For instance, photonic crystals and metasurfaces are sensitive to incident angle. Quantum dot materials suffers from light fluorescence loss and low throughput. To address these challenges, some researchers have investigated the use of mixed materials for spectral modulation, aiming to overcome the limitations of individual materials.The reconstruction of compressed signals can be described as a nonlinear optimization problem, where the selection of the regularization term is critical to effective signal recovery. Conventional regularization techniques include sparse regularization, total variation (TV) regularization, and low-rank structure priors, and so on. With the rapid development of deep learning technologies, spectral imaging has increasingly relied on deep learning as a prominent reconstruction method. Deep learning-based spectral reconstruction is several orders of magnitude faster than compressed sensing and offers superior noise tolerance. The numerous advantages of deep learning have greatly expanded the practical applications of computational spectral imagers. However, despite its superior reconstruction performance compared to compressed sensing, deep learning methods require large datasets for training. The selection of training data and the tuning of model parameters can significantly influence reconstruction outcomes, especially when noise levels are high or when the dataset is limited. In cases where the number of training samples is insufficient, the model's ability to generalize to unseen data is compromised, resulting in poor reconstruction performance for samples outside the training set. This lack of generalization remains a significant challenge for end-to-end reconstruction methods. The continuous advancement of spectral response methods has significantly contributed to the development of computational spectral imaging systems characterized by miniaturization, high spatial-spectral resolution, and enhanced throughput. However, existing spectral response techniques exhibit several limitations, including angle sensitivity, low transmittance, and similar filter curves. Moreover, most research in this field remains confined to laboratory environments or specific scenarios, leaving a considerable gap between current methods and practical applications. Efforts have been made to integrate different spectral modulation techniques to mitigate the limitations of individual spectral modulation methods. Additionally, the application of deep learning has notably improved reconstruction performance. Nevertheless, the generalization and robustness of these approaches require further validation. Despite the persistent challenges associated with spectral imaging technology based on spectral response, advancements in optics, material science, computational power, and related fields offer promising prospects. We believe that computational spectral technology leveraging broadband filtering will eventually overcome these challenges and achieve widespread applicability.