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Cryptographic Hash Functions have a distinct importance in the area of Network Security or Internet Security as compare to Symmetric and Public Key Encryption-Decryption techniques. Major issues primarily which resolved by any hash algorithm, are to manage the Integrity and Authenticity of messages which are to be transmitting between communicating parties and users with digital signatures. Hash function also utilized for fixed length secrect key generation in Symmetric and Public Key Cryptosystems. Different level of security provided by different algorithms depending on how difficult is to break them. The most well-known hash algorithms are MD4, MD5, SHA, JH, Skein, Grøstl, Blake, Hamsi, Fugue, Crush, Whirlpool, Tav etc. In this paper we are discussing importance of hash functions, hash functions widely used in networking, most importantly various Attacks applicable on hash functions and compression functions utilized by hash functions.