We consider a simple model of a random temporal graph, obtained by assigning to every edge of an Erdős–Rényi random graph G_n,p a uniformly random presence time in the real interval [0, 1]. We study several connectivity properties of this random temporal graph model and uncover a surprisingly regular sequence of sharp thresholds at which these different levels of connectivity are reached. Finally, we discuss how our results can be transferred to other random temporal graph models. Based on joint work with Arnaud Casteigts, Michael Raskin, and Viktor Zamaraev.