We have studied the electromagnetic field distribution around metallic nanostructures using a scanning near-field optical microscope. The probe is a small fluorescent particle settled at the extremity of a tungsten tip. If the sample is illuminated, the fluorescence emitted by the particle varies with its position on the surface, giving a representation of the electromagnetic field distribution. The nanostructures, which are gold nanoparticles and nanoapertures in a thin gold film have been imaged as a function of the incident light polarization direction. In the case of gold nanoparticles, an increase of the field intensity is visible when the probe is localized on the nanostructure. This field distribution is elongated in the direction of the incident light polarization. In the case of nanoholes, the images show that, in addition to the transmission through the holes, some light is localized between adjacent holes. This light localization, which is strongly dependent on the polarization direction, is attributed to plasmon polariton waves emitted by the holes in the metal film.