A theoretical overview of the phenomenon of Bose-Einstein condensation in dilute gases confined in harmonic traps is provided. The main features exhibited by condensation in both momentum and co-ordinate space are investigated, with special emphasis on the role played by two-body interactions, which are treated in mean-field theory. Despite the dilute nature of these gases, interactions are found to deeply modify the ground state as well as the dynamic properties of the system, in excellent agreement with the available experimental results. The temperature dependence of the condensate fraction and of other thermodynamic functions is discussed. The occurrence of relevant length and energy scales, yielding a scaling behavior in the thermodynamic limit, is pointed out. Superfluidity effects, such as the existence of quantized vortices and the reduction of the moment of inertia, are explored, together with other important consequences of coherence, like the Josephson effect and interference phenomena. The accuracy and the limits of the mean-field approach are also discussed.