Causation is a phenomenon of (general) relativity, giving a natural partial order to events. The equations of physics constrain what phenomena they can explain in an acausal fashion: neither do equations cause physics to happen a certain way, nor do observations change a model by fitting it well/poorly. — my earlier comment
I agree with and have upvoted all prior answers. This is an invited answer focusing on causal sets (WP, nLab).
Quoting nLab, a causet "is a concept with an attitude: In itself it is just a partially ordered set (or poset, for short), but meant to be understood as a set of spacetime events subject to the relation of causality." Formally, a causet is a partial order where every interval is finite.
This condition is subtle enough to need explanation. The interval has finitely many smoothly-deformable paths, and its cardinality is related to the topology of spacetime. For example, consider a room with two entrances and the events "I am outside the room" and (later) "I am inside the room". I can walk through either entrance, but I can't smoothly deform my walking-path from one entrance to another, so the interval between those events has cardinality two.
An immediate consequence of this framing is that the laws of physics, particularly those which include time, are outside of causality. To be causal is to be embedded within some sort of smooth Lorentzian space.