For a brief overview here, we note that hash functions are often divided into three classes according to their design:

those built around block ciphers,

those which use modular arithmetic, and

those which have what is termed a "dedicated" design.

By building a hash function around a block cipher, it is intended that by using a well-trusted block cipher such as DES a secure and well-trusted hash function can be obtained. The so-called Davies-Meyer hash function is an example of a hash function built around the use of DES.