The cryptographic methods used today are the outcome of an extremely long history of development. Cryptographic hash functions play a big role in modern world computer networks, protection of data integrity and in telecommunication. We are using hash functions every day without even realizing such as bank transactions, website logins, daily phone communications and many more to secure and protect our privacy. Hash function is a function that compresses an arbitrary large message into a fixed size message digest. Many types of hash functions have been introduced over the last three decades, but only the hash functions based on block ciphers and the dedicated ones are the most widely used in many of the cryptographic applications. This thesis presents a study of different types of hash functions and their properties, different types of attacks on the hash functions and structural weaknesses of the hash functions. It also consists of explanation of the working process of the already existing hash functions and their security analysis and Merkle-Damgård construction with its related constructions and attacks that have done on Merkle-Damgård construction. In addition, the Keccak hash algorithm, its construction, its security analysis and attacks on Keccak.