Multispectral cameras collect image data with a greater number of spectral channels than traditional trichromatic sensors, thus providing spectral information at a higher level of detail. Such data are useful in various fields, such as remote sensing, materials science, biophotonics, and environmental monitoring. The massive scale of multispectral data-at high resolutions in the spectral, spatial, and temporal dimensions-has long presented a major challenge in spectrometer design. With recent developments in sampling theory, this problem has become more manageable through use of undersampling and constrained reconstruction techniques. This article presents an overview of these state-of-the-art multispectral acquisition systems, with a particular focus on snapshot multispectral capture, from a signal processing perspective. We propose that undersampling-based multispectral cameras can be understood and compared by examining the efficiency of their sampling schemes, which we formulate as the spectral sensing coherence information between their sensing matrices and spectrum-specific bases learned from a large-scale multispectral image database. We analyze existing snapshot multispectral cameras in this manner, and additionally discuss their optical performance in terms of light throughput and system complexity.