In the present work the most recent models for the prediction of the strain release and of the distribution of misfitdislocations in continuously graded layer heterostructures, to be used as buffer layers to limit the propagation of dislocations at the top of the structure and to achieve a desired final lattice parameter suitable for the unstrained growth of a mismatched material, are presented and discussed. The results of transmission electron microscopy. X-ray diffraction and Rutherford Backscattering investigations on InGaAs/GaAs structures with different continuously graded profiles grown by molecular beam epitaxy technique are reported and compared with the predictions of the different models. Different dislocation distributions in the buffer layers depending on the composition gradient have been observed by transmission microscopy. The distributions of dislocations are discussed in term of actual models describing the strain release in continuously graded structures. These models are not able to determine accurately at the same time the residual strain and the dislocation distribution in the structures.  In particular the problem of measuring the threading dislocation densities is discussed. Lattice tilts between the substrate lattice and the buffer layer lattice as large as 0.5 degree were detected by high resolution X-ray diffraction and ion channeling techniques. Since the lattice tilts are determined by the distribution of the Burgers vectors of the misfit dislocations, a mechanism of strain release and dislocation generation at the sample surface is supposed.  Lattice tilts varying with the position on the sample have been observed in all the samples. The tilt changes coherently along the sample surface producing in average a concave curvature of the buffer layer, though the tilt distribution was found to be not continuous in several cases. The X-ray topography observations showed that the layers are divided in large domains with different average lattice tilt and that these domains are not correlated with the dislocation distribution of the undoped semi-insulating Czochralski GaAs substrate.