In 1939, T. Carleman introduced some energy estimates with exponential weights to prove a strong unique continuation property for some elliptic partial differential equations (PDEs for short) in dimension two. This type of weighted energy estimates, now referred to as Carleman estimates, have become one of the major tools in the study of unique continuation property, inverse problems and control theory for PDEs . In this talk, I will introduce the ideas of Carleman estimates and show how Carleman estimates play important roles in studying control problems of wave equation and heat equation.