In Chap. 9 we have seen how to manipulate a two-level atom by using oscillating electric field treated as classical or quantized entities. In that case the atoms usually move through a cavity which contains the field. A complementary approach consists in fixing the position of the atoms in the space and address suitably tuned laser beams in order to control their electronic levels and to perform quantum operations. In this last case, the atoms are ionized and trapped by using both static and time-varying electric fields: now one can exploit the electronic levels of the ions to encode the qubits’ state, but also their collective quantized motion, that allows to implement two-qubit gates. In this chapter we review the basic working principle of a linear Paul trap, which is used to confine a chain of ions, we derive the quantum Hamiltonian describing their quantized motion and we investigate their manipulation through suitable classical laser pulses. We eventually show how to perform universal quantum computation with trapped ions.