Lipids are stored in specialized fatty tissue called adipose tissue. In the adipose tissue, the lipids are stored in specialized cells called adipocytes, which typically form a cushioning and insulation layer under the skin and around the organs. 

Adipocytes are capable of storing almost unlimited quantities of lipids in cell organelles known as lipid droplets. Lipid droplets can grow to a very large size, which supports the extensive storage capacity of adipocytes.