Most processes in nature are nonequilibrium (NEQ) processes, which include key dynamic processes in biological cells and social networks, as well as usual physical phenomena. Recently, there has been a considerable progress on the issue of the thermodynamic second law, which is known as the law of entropy increase or irreversibility. In particular, a novel symmetry known as the Gallavotti-Cohen symmetry is found in NEQ fluctuations, which leads to so-called fluctuation theorems. The thermodynamic second law is a simple corollary of fluctuation theorems, from which one can predict quantitatively how often NEQ processes violate the law of entropy increase. Violations disappear in the thermodynamic limit, but can be observed reasonably well in small systems. In this talk, I will briefly introduce the fluctuation theorems and discuss about stochastic thermodynamics, which is a key framework for these theorems and provides a new perspective on entropy in NEQ processes.