  The spacetime discreteness of causal set theory has enabled the formulation
of novel spacetime dynamics. In these so-called "growth" dynamics, a causal set
spacetime is generated probabilistically by means of a random walk on certain
tree structures. The first growth dynamics - the Classical Sequential Growth
models - were proposed more than two decades ago and their study has furthered
our understanding of general covariance and covariant observables within causal
set theory. In this setting, labels take the place of spacetime coordinates so
that general covariance takes the form of label-invariance and covariant
observables are those order-theoretic properties of the causal set which are
label-independent. In recent years, these insights have led to a new
formulation of growth dynamics which makes no reference to labels. Here we
present an overview of these (manifestly) covariant growth dynamics.
