The human is a social being which has an innate tendency to communicate. In today's world, most of the communication takes place on social media. There is a multitude of social networks which attract masses of people who communicate in that way, share different kinds of content, data and information. In the Republic of Croatia, that is mainly done on two social networks: Facebook and Instagram. This thesis contains the analysis of these two social networks, as well as the method of creating a user account which demands conclusion of a contract of sorts between the user, who acquires the user account, and the company which manages the social network. The central section of the thesis contains a review of a series of regulations and laws which are related to the information society and infrastructure. However, there is no specific law in the Republic of Croatia that is related specifically to social networks, even though it is an area in which more and more occurrences of unwanted behavior and activities occur. The final part of the thesis contains a deliberation on the matter of adopting a law which would refer specifically to social networks according to the example of a law adopted in Germany.