This work presents the results of a detailed study of the statistical and physical properties of binary ultracool dwarfs and brown dwarfs (spectral type later than M7). As for the statistical properties, we found that the frequency of binaries among ultracool objects is significantly lower than for earlier type objects, with a lower limit at 10--15% in the field, and 10% in the Pleiades Open cluster. While we were sensitive to systems with separations up to 100 A.U, we did not find any multiple system with separation greater than 20 A.U. At even larger separations, no wide binaries were reported by the all sky surveys such as 2MASS, DENIS or SDSS. The distribution of separations looks similar to that of F and G dwarfs (Gaussian), but with a peak at 4--8 A.U. Although we were sensitive to mass ratios down to 0.65, we found most of the objects to have mass ratios larger than 0.85. This latter result needs to be confirmed by further statistical studies on well defined statistical samples. Although the sample of known binaries in the Pleiades is too small for a similar analysis, we note that the binary frequency, the distributions of mass ratio and separations are similar, indicating that the properties of binary brown dwarfs might not depend on the age and environment after 125 Myr. Finally, although we did not have the opportunity to perform a similar statistical study in a star forming region, we report the first detection of a young binary brown dwarf with a disk in the R-CrA association. These results provide strong constraints on the models of ultracool dwarf formation and evolution. The binary frequency is currently not reproduced by any of these models. The models of ejection could explain the lack of binaries wider than 20 A.U and the apparent preference for equal mass systems, but they predict a much lower binary frequency. The model assuming that brown dwarfs form in a smilar way than stars could reproduce the binary frequency we observe, but could not explain the distributions of separation and mass ratio. More efforts are required on the theoretical side in order to better explain the observed properties, and on the observational side to give new and improved constraints. As for the physical properties, our observations lead to the discovery of a short period binary L dwarf. Observations at high angular resolution spread over 4 years allowed us to follow the companion on 60% of its orbit. For the first time, we were then able to compute the orbital parameters and total mass of such a very low mass object. In the near future, similar studies should enable us to calibrate brown dwarf mass and luminosity models. Using high angular resolution spectroscopy, we were able to disentangle the spectra of the individual components of 4 binary ultracool dwarfs and to compute their spectral types. Two binaries have companions with spectral types significantly later than their primary (by 3 to 4 spectral subclasses), allowing us to compare the evolution of their effective temperature and atmosphere. Finally, using our high angular resolution images, we were able to detect a possible third component in one of the binaries of our sample.