Live-cell fluorescence spectral imaging is an evolving modality of microscopy that uses specific properties of fluorophores, such as excitation or emission spectra, to detect multiple molecules and structures in intact cells. The main challenge of analyzing live-cell fluorescence spectral imaging data is the precise quantification of fluorescent molecules despite the weak signals and high noise found when imaging living cells under non-phototoxic conditions. Beyond the optimization of fluorophores and microscopy setups, quantifying multiple fluorophores requires algorithms that separate or unmix the contributions of the numerous fluorescent signals recorded at the single pixel level. This review aims to provide both the experimental scientist and the data analyst with a straightforward description of the evolution of spectral unmixing algorithms for fluorescence live-cell imaging. We show how the initial systems of linear equations used to determine the concentration of fluorophores in a pixel progressively evolved into matrix factorization, clustering, and deep learning approaches. We outline potential future trends on combining fluorescence spectral imaging with label-free detection methods, fluorescence lifetime imaging, and deep learning image analysis.