Over the past twenty years, the internet has been considered one of the most important tools for the process of globalization, distribution of knowledge and as a fundamental tool for social-, economic- and cultural development. It is the primary means of communication, since we can receive information almost immediately in real time. In addition to this, the security of information traveling over the internet is also a point of much importance for companies that need more appropriate solutions. Since with the increase of internet users, there is also an increase of malicious users interested in getting information, or steal, to get some kind of benefit or even harm others through network attacks. This paper deals with the study of two such major attacks originated from DoS (Denial of Service): (i) DDoS (Distributed Denial of Service); and (ii) DRDoS (Distributed Reflection Denial of Service). Both attacks are top security issues, which affect networks and interrupt service to legitimate users. This paper is divided into six chapters that will facilitate the understanding of this problem. This paper also demonstrates the problems encountered in the defense of DDoS attacks and DRDoS. For this, it shows the source of the problem, its variations and some solutions (most currently used) to detect and mitigate these attacks.