The gallbladder has ducts connected to both the liver and the duodenum:

1. Cystic duct: Connects the gallbladder to the common hepatic duct, which comes from the liver.

2. Common bile duct: Formed by the junction of the cystic duct and common hepatic duct, connects to the duodenum (the first part of the small intestine).

Bile produced by the liver flows through the hepatic ducts into the gallbladder, where it is stored and concentrated. When food enters the duodenum, the gallbladder contracts, releasing bile through the common bile duct into the duodenum to aid in fat digestion.