Because of the inherent nonlocalityNonlocality of continuumlikeContinuumlike causal set causal sets, CST dynamics is best suited to the covariant path integral or sum-over-histories framework. The continuum-inspired CST partition function is a discrete sum over causal sets with complex weights given by the discrete BDG actionBDG action. An important analytic result for the theory is that the BDG action suppresses the most entropically dominant, non-continuumlike contributions for large n, while providing a minimum discreteness scale of order the Planck scale in all dimensions. The partition function can be analytically continued into a theory of Lorentzian statistical geometry and studied numerically, by Markov Chain Monte Carlo techniques. The dimensionally restricted cases in \(d=2\) and \(d=3\) exhibit a first order phase transition between a continuumlike and a noncontinuumlike phase, which can be interpreted in terms of a Hartle-Hawking wave function. A more fundamental dynamics based on purely order theoretic principles is the Rideout-Sorkin sequential growthSequential growth models in which a causal set is grown element by element. The dynamics is Markovian and satisfies internal temporality, covariance and spectator independence. It is defined by a measure tripleMeasure triple (either classical or quantum) where the observablesCovariant observables (or beablesBeables) are events in a covariant-sigma algebra, some of which have cosmological significance.