This chapter covers the various problems arising in the estimation of the integrated volatility, in the idealized situation where the process is observed without error (no microstructure noise) and along a regular observation scheme. In this case the situation is quite well understood, although not totally straightforward when the process has jumps. In this chapter, our aim is to estimate the (random) quantity Csubscript T at a given time T, upon observing the process X without error, at the discrete times i Δₙ for i = 0, 1, … , [T/Δₙ], and when the mesh Δₙ of the observation scheme goes to 0. Since the initial value X₀ gives no information at all on Csubscript T, we can equivalently suppose that we observe the returns, or log-returns.