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Internet routing is based on the destination address and a shortest path algorithm, this leads to some links are congested because the same paths are selected for many communications. On the other hand, constraint based algorithms select the path based on a set of requirements that allows choosing the most optimal path for a specific set of constraints, solving the problem of the shortest path routing and providing additional benefits such as support QoS and traffic engineering. In the literature, it has been shown that the processes with traffic engineering objectives are NP-hard, and for quality of service are NP-complete, it allows making heuristic algorithms proposals because this is an open issue. Therefore, this article provides an overview of the constraint based algorithms proposed as a solution to the problem of conventional Internet routing in the last 15 years. This study has been organized into three categories according to the goals for each proposal. These categories were targeted in Internet current issues that are Traffic Engineering and Quality of Service support. A brief description of each algorithm is presented, highlighting their objectives and constraints. It is very important to highlight that to propose solutions to these issues remains a challenge and is an open issue, for this reason to have a knowledge of the taxonomy of these algorithms and objectives allows us to propose new alternatives to routing for next generation networks, with new demands on their services. [ABSTRACT FROM AUTHOR]