Described are swivel systems and swivel assemblies for connecting a vacuum appliance to a vacuum accessory. The assemblies can include first and second arcuate members that each includes a tab and a receiving section so the latter can receive the other member's tab. The assembly can be adapted to be coupled to the accessory to permit the appliance to pivot relative to the accessory about two independent axes. The swivel system can include a vacuum adapter and a connector adapted to permit the vacuum adapter to pivot about a vacuum accessory. A plenum chamber can be formed in the adapter that is in fluid communication with one or more vacuum hoses to balance the airflow within the adapter. With the swivel systems and assemblies described herein, the versatility and efficiency of vacuum appliances and other tools can be improved through their multi-axes rotational capabilities and balanced airflow configurations.