If your Rust server is listed in the control panel as Running, but you can't connect after several minutes via Steam or within the game itself, please trigger a Steam Update by clicking on Steam Update on the left menu within the control panel.
If you run Oxide on your server, you will need to update Oxide through the Updates icon on the left menu within the control panel after the Steam update is done. This is required to occur because a Steam update overwrites files that launch Oxide at startup.
If you server still does not come online after 5 minutes, please review the log.txt file in your server's main directory for troubleshooting codes or contact support.