Abstract: In 1915 G.H Hardy needed an estimate for arithmetic means to find a proof of Hilbert's inequality for sequences, a continuous version of that inequality followed in 1925. Since then, extensions have been made in many directions; more general domains, weighted norm inequalities, general measures, among others. In this talk we will review the classic statement of Hardy's original inequality. We will explore some of the extensions of this important inequality and review some of its implications, such as, Sobolev inequalities and boundedness of the Fourier transform in weighted Lorentz spaces.