How are fats digested in our bodies? Where does this process take place?

Emulsification of large fat globules by the salt of bile [secreted by liver] into smaller micelles, fat-digesting lipase enzyme in pancreatic juice and intestinal juices digest the fat in micelles into triacylglycerols and then fatty acids and glycerol which are absorbed by intestinal mucosa. This process takes place in the small intestine.