We say that a dynamical system satisfies shadowing property if for any pseudotrajectory there exists an exact trajectory that is pointwise close to it. This property was introduced by Anosov in 1970th and plays an important role in the theory of dynamical systems. Shadowing property is known to have strong connections with hyperbolicity and structural stability. In this talk I will give an overview of classical results in shadowing theory and will present a new proof of Anosov shadowing lemma.