Darren Melrose, 18, Jordan Parry and Billy Jo Revie, both 16, and a 16-year-old girl who cannot be named for legal reasons, are alleged to have broken into the Clutha Vaults in Stockwell Street on December 17.
They are accused of stealing items from the Glasgow pub.
Melrose, and Parry, from Glasgow, appeared in private at Glasgow Sheriff Court from custody. The 16-year-old and Revie, from Glasgow, walked into the court for their private appearance.
All four appeared separately where they made no plea or declaration and were all remanded in custody by sheriff Brian Adair.
They will appear for a committal hearing later and are expected to spend Christmas in detention.