In the literature, complex-valued random fields were initially employed to characterize the spatial evolution of vector data, while the temporal dimension was typically treated separately or modeled using time-dependent complex covariance structures. Nevertheless, as in the real case, extending the complex formalism to a unified spatiotemporal framework and developing new classes of spatiotemporal complex covariance models are of clear interest to researchers, driven in part by the rapid increase in environmental vector observations collected over space and time. This contribution outlines the foundational elements of the complex spatiotemporal random field framework and describes how several spatiotemporal complex-valued covariance families can be derived from the spatial setting as well as from positive mixtures of infinite components or a convolution of the real part.