In this talk, we begin with a motivation for and brief introduction to causal graphical modeling of time series. We then discuss two recent works in this area. First, a complete characterization of a class of graphical models for describing lag-resolved causal relationships in the presence of latent confounders. This characterization sheds new light on existing time series causal discovery algorithms and shows that there is room for stronger identifiability results than previously thought. Second, a method for projecting infinite time series graphs with time-invariant edges to finite marginals graphs. We argue that the construction of these marginal graphs is a big step towards a method-agnostic generalization of causal effect identifiability results to time series.