Erosion by water is a natural phenomenon that modeled many famous places worldwide such as Etretat Arch in France but it can become environmentally problematic when receiving waters are affected by untreated waste waters and even catastrophic when dams are affected. For example, in 2010, the Del Dique Channel in Columbia was broken by erosion phenomenon, letting more than 185,000 without any protection and costing more than 250 millions of euros. In the same time it has been proved that sediments from sewer channels highly contribute to pollutant discharged as they are eroded during storm events. But existing civil engineering structures are huge and complex so it appears very difficult to reproduce them in a laboratory so it is of crucial interest to be able to measure their resistance to erosion in their real context. This paper aims at making a state of the art of how to measure erosion under water. First of all, this paper remembers what erosion and erosion rate are. Then a short presentation of the published erosion laws is given and their limits are discussed. The paper ends with a presentation of some devices presented into the scientific or professional literature.