Recently, Balogh-Morris-Samotij and Saxton-Thomason developed a method of counting independent sets in hypergraphs. During the talk, I show a recent application of the method; solving the following Erdos problem: What is the number of maximal triangle-free graphs? If there is some extra time in the talk, I will survey some other recent applications. These applications are partly joint with Das, Delcourt, Liu, Mycroft, Petrickova, Sharifzadeh and Treglown.