Nanoscience and nanotechnology are tremendously increasing fields of research that aim at producing, characterizing and understanding nanoobjects and assemblies of nanoobjects. Their new physical or chemical properties, which arise from confinement effects, intimately depend on their morphological properties, i.e. their shapes, their sizes and their spatial organization. This calls for dedicated morphological characterization tools, among which is the Grazing Incidence Small Angle X-Ray Scattering (GISAXS). This reciprocal space technique has emerged in the last two decades as a powerful tool that allows investigating in a non-destructive way the morphological properties from one to billions of nanoparticles, either on a surface, or embedded in a matrix, with sizes ranging from 1 nm to several microns. The advantages of the technique are that it is non-destructive; it yields statistical information averaged on a large number of nanoparticles; it allows probing both the surface or deep below it, by changing the incident angle of the X-ray beam; it can be used in very different sample environments, in particular in situ in the course of a given process such as growth, annealing, gas exposure; and it may be given chemical sensitivity by use of anomalous scattering. This report presents a review of the GISAXS technique, from experimental issues to the theories underlying the data analysis, with a wealth of examples. The physical morphological information contained in GISAXS data and its analysis are presented in simple terms, introducing the notions of particle form factor and interference function, together with the different cases encountered according to the size/shape dispersion. The theoretical background of X-ray diffuse scattering under grazing incidence is presented in a general way, and then applied to the particular case of grazing incidence small angle X-ray scattering from assemblies of particles either on a substrate, or buried below it. Most of the GISAXS measurements published to date are reported, covering the fields of ex situ studies of embedded metallic nanoparticles, granular multilayered systems, implanted systems, embedded or stacked or deposited semi-conductor nanostructures, porous materials and copolymer thin films. A special emphasis is brought on in situ experiments, performed either in ultra-high vacuum during nanoparticle growth by molecular beam epitaxy, or in gas-reactors during catalytic reactions. This covers a very broad field, from (i) the 3D island (Volmer-Weber) growth of metals on oxides surfaces to (ii) the organized growth of metals on surfaces that are nanopatterned either by surface reconstruction or by underlying dislocation networks or by deposit-induced nanofacetting, to (iii) the in situ investigation of the self-organized Stranski-Krastanow hetero-epitaxial growth of semi-conductor quantum dots on semi-conductor surfaces, or (iv) the in situ surface nanopatterning by ion bombardment. Many examples are discussed in detail, to illustrate the large diversity of systems and morphologies that can be addressed as well as the different analysis issues and the conclusions of the technique in terms of growth mode.