When a liquid droplet is put onto a surface, two situations distinguishable by the contact angle may result. If the contact angle is zero, the droplet spreads across the surface, a situation referred to as complete wetting. If the contact angle is between zero and 180ะ, the droplet does not spread, a situation called partial wetting. A wetting transition is a surface phase ลฝ . transition from partial to complete wetting. The wetting transition is generally first-order discontinuous , implying a discontinuity in the first derivative of the surface free energy. As a consequence, at the transition a discontinuous jump in film thickness occurs from a molecularly thin to a thick film. We show here that the first-order nature of the transition can lead to the observation of metastable surface states and an accompanying hysteresis. The second part of this review deals with the exceptions to the first-order nature of the wetting transition. Two different types of continuous or critical wetting transitions have been reported, for which a discontinuity in a higher derivative of the surface free energy occurs. This consequently leads to a continuous divergence of the film thickness. The first type is long-range critical wetting, due to the long-range van der Waals forces. We show that this transition is preceded by the usual first-order wetting transition, which, however, is not achieved completely. This leads to the existence of a new intermediate wetting state, in which droplets coexist with a mesoscopic film: frustrated complete wetting. The film thickness diverges continuously from this mesoscopic film to a thick film. The second type of continuous transition is short-range critical wetting, for which the layer thickness diverges continuously all the way from a microscopic to a macroscopically thick film. This transition is interesting, as renormalization-group studies predict non-universal behaviour for the critical exponents characterizing the wetting transition. The experimental results, however, show mean field behaviour, the reason for which remains unclear.