1. A computer program product for replicating objects from a source storage managed by a source server to a target storage managed by a target server, the computer program product comprising a computer readable storage medium having computer readable program code embodied therein that executes to cause the source server to perform operations, the operations comprising: maintaining, at the source server, a replication rule specifying a condition for a replication attribute and a replication action to take if the condition with respect to the replication attribute is satisfied, wherein multiple of the objects are capable of having attribute values that satisfy the condition of the replication attribute, wherein the replication action indicates to include or exclude the object having an attribute value for the replication attribute that satisfies the condition; initiating an operation to replicate objects at the source server to the target server; for each of the objects, applying the replication rule by performing: determining an attribute value of the object corresponding to the replication attribute in the replication rule; determining whether the determined attribute value satisfies the condition for the replication attribute defined in the determined replication rule; performing the replication action on the object in response to determining that the determined attribute value satisfies the condition for the replication attribute; and adding an identifier of the object to a replication list satisfying the condition in response to the replication action indicating to replicate the object; and copying the objects indicated in the replication list to the target server.