This paper reviews aspects of nonlinear optical spectroscopy of interfaces. The emphasis is put on second-order nonlinear optical techniques, such as sum-frequency generation (SFG), which possess intrinsic surface or interface selectivity and can therefore be used to probe buried interfaces accessible by light. The basic concepts of the second-order nonlinear response of surfaces and interfaces are given. While SFG in the ultraviolet-visible range allows one to achieve surface-specific electronic spectroscopy, infrared-visible SFG spectroscopy allows one to have access to absolute vibrational spectra of adsorbates at an interface. The main experimental schemes commonly employed are described. Selected experimental examples are given for studies of liquid surfaces and interfaces, polymer surfaces and interfaces, solid surfaces under ultra-high vacuum conditions or in inert atmospheres, solid-gas interfaces, solid-liquid interfaces and solid-solid interfaces. Both frequency-resolved studies and time-domain measurements are addressed.

Phone: +33 1 69 15 32 75; Fax: +33 1 69 15 33 28 RECEIVED DATE (to be automatically inserted after your manuscript is accepted if required according to the journal that you are submitting your paper to) TITLE RUNNING HEAD Non uniqueness of parameters in NLO spectroscopiesAbstract Experimental data from second-order nonlinear optical spectroscopies (SFG, DFG, SHG) provide parameters relevant to the physical chemistry of interfaces and thin films. We show that there are in general 2 N or 2 N-1 equivalent sets of parameters to fit an experimental curve comprising N resonant features, of vibrational or electronic origin for example. We provide the algorithm to calculate these sets, among which the most appropriate has to be selected. The main consequences deal with the existence of "ghost resonances", the need of a critical analysis of fit results and the procedure to search for better sets of parameters coherent with applied constraints.