Tightly focused femtosecond laser pulses can be used to alter the refractive index of virtually all optical glasses. As the laser-induced modification is spatially limited to the focal volume of the writing beam, this technique enables the fabrication of fully three-dimensional photonic structures and devices that are automatically embedded within the host material. While it is well understood that the laser-material interaction process is initiated by nonlinear, typically multiphoton absorption, the actual mechanism that results in an increase or sometimes decrease of the refractive index of the glass strongly depends on the composition of the material and the process parameters and is still subject to scientific studies. In this paper, we present an overview of our recent work aimed at uncovering the physical and chemical processes that contribute to the observed material modification. Raman microscopy and electron microprobe analysis was used to study the induced modifications that occur within the glass matrix and the influence of atomic species migration forced by the femtosecond laser writing beam. In particular, we concentrate on borosilicate, heavy metal fluoride and phosphate glasses. We believe that our results represent an important step towards the development of engineered glass types that are ideally suited for the fabrication of photonic devices via the femtosecond laser direct write technique.