In this talk, we will give an overview of several methods and ideas on how to find regular subgraphs in graphs with some average degree.

We will discuss the still widely opened Erdos-Rado Sunflower Conjecture and we will give a sketch of a recent proof of the Erdos-Szemeredi Conjecture. More precisely, we will show that any graph on n vertices and average degree $C(k)\log(\log(n))$ contains a $k$-regular induced subgraph, which is tight up to the implied constant as shown by a classical construction of Erdos, Pyber and Szemeredi.