In this review paper, we present some mathematical aspects that have been influenced by the emergence and development of certain cryptographic systems, as for example public key cryptosystem RSA and symmetric key cryptosystems DES. In addition, we give some examples of situations that appeared in various historical periods that were influenced by the use of secret codes or vice versa: how these events influenced the appearance of certain cryptographic systems, tools or devices, some of them being considered indispensable in our days.