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 non-transitory 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 hierarchical arrangement of at least first and second level replication rules, wherein each of the first and second level replication rules in the hierarchy specifies a condition for a replication attribute and a replication action to take if the condition with respect to the replication attribute is satisfied, wherein the replication action in the first and second level replication rules of the hierarchy indicates to include or exclude each of the objects 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 first and second level replication rules in an order determined by the hierarchy until an attribute value of the object satisfies a condition of a replication attribute defined in the replication rule being applied according to the order 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.