Worst-case scenario: the UEd Goblin wipes the map and burns down your house.
There are three types of message the engine might send over the network in order to support replication:
Whenever the server decides that an actor has become relevant to a particular client, the server instructs the client to create an actor of that class and initialize it either with its client-side default properties (in the case of a newly-created actor) or with the values currently held by the server.
Whenever a variable changes, if the condition in the replication block is met, and subject to the bNetUpdateFrequency of the actor, the server queues a network message that instructs the client to change a variable to the new value. Clients can also replicate some variables to the server, in the case of inputs, etc. Variables waiting to be replicated enter a queue and are replicated when bandwidth is available, depending on the actor's bNetPriority.
This is simply a remote function call. The engine transmits a request for the remote end to call a function. This can also be used to call a function on the server based on the client's input. See Replicated Function.