Concrete rainwater tanks are expensive, but ideal for underground water storage or when large quantities of water need storing. They are often long lasting, although cracking will eventually happen over time depending upon the strength of concrete and level of reinforced with steel.
One benefit, but also disadvantage, is the lime that is found in concrete. It is an advantage because it reduces the acidity of rainwater which prevents copper leaking into the water sitting in your copper pipe plumbing. A disadvantage is that lime in your rainwater can taste quite bitter if drinking.