We study the problem of causal discovery from event sequences, with the goal of recovering the underlying causal graph and causal mechanisms over different types of events. To this end, we introduce a new causal model, where individual events of the cause variable trigger events of the effect variable with dynamic delays. We show that in contrast to existing methods based on Granger causality, our model is identifiable for both instant and delayed effects.We base our approach on the Algorithmic Markov Condition, by which we identify the true causal network as the one that minimizes the Kolmogorov complexity. As the Kolmogorov complexity is not computable, we instantiate our model via the Minimum Description Length (MDL) principle. We show our score is consistent and identifies the true causal directions. To discover good causal graphs in practice we introduce the Cascade algorithm, which adds edges in topological order. The evaluation of Cascade on synthetic and real-world datasets shows it works well in practice, outperforming existing methods.