<p>In many fields of science, multivariate spatio-temporal data can exhibit quite complex dependence structures between the variables and over the domain. Many approaches exist to model such data and usually their starting point is the matrix-valued covariance function (CF). The well-established space-time linear coregionalization model (ST-LCM) and more recently the space-time blind source separation-based model (ST-BSS) can easily support the modeling stage, since they rely on the univariate analysis of latent components. Although they have been developed within distinct backgrounds and some differences between them can be highlighted, they also share various similarities from a theoretical and practical point of view. A critical review of the hypothesis, properties and characteristics of the two approaches is then proposed and a comparison of their performances is provided through a real dataset analysis and a simulation study.</p>