The paper introduces the ARTIVA (Auto Regressive Time VArying) formalism, a statistical modeling framework and inferential procedure for learning temporally varying gene-regulation networks from biological time-course expression data. ARTIVA simultaneously infers the topology of a regulatory network and how it changes over time, allowing for the recovery of the chronology of regulatory associations for individual genes involved in specific biological processes. The method is evaluated on simulated data and applied to two biological scenarios: the developmental stages of Drosophila melanogaster and the response of Saccharomyces cerevisiae to benomyl poisoning. The results demonstrate that ARTIVA effectively recovers essential temporal dependencies in biological systems from transcriptional data, providing a detailed understanding of the function and dynamics of complex biological systems.The paper introduces the ARTIVA (Auto Regressive Time VArying) formalism, a statistical modeling framework and inferential procedure for learning temporally varying gene-regulation networks from biological time-course expression data. ARTIVA simultaneously infers the topology of a regulatory network and how it changes over time, allowing for the recovery of the chronology of regulatory associations for individual genes involved in specific biological processes. The method is evaluated on simulated data and applied to two biological scenarios: the developmental stages of Drosophila melanogaster and the response of Saccharomyces cerevisiae to benomyl poisoning. The results demonstrate that ARTIVA effectively recovers essential temporal dependencies in biological systems from transcriptional data, providing a detailed understanding of the function and dynamics of complex biological systems.