Ultrashort laser pulses are a powerful tool for modifying the structure and properties of transparent materials. Depending on material properties and irradiation conditions, a wide variety of modifications can be induced such as surface and bulk periodic structures (nanogratings), densification with associated refractive index change, microvoids and void chains, phase transitions, etc. This gives rise to numerous technological applications based on 3D photonic structures in bulk optical materials (waveguides, Bragg gratings, Fresnel zone plates, rewritable optical memories, and others). Among transparent materials, optical glasses are of prime importance for optoelectronics and photonics due to their relatively low cost, processability, and possibility of governing refractive index and inducing optical anisotropy. The physics behind laser-induced glass modification is extremely rich and involves the multiplicity of the consecutive processes initiated by radiation absorption during the laser pulse and extending to millisecond time scales when the final structure becomes .frozen. in the glass matrix. While tremendous achievements have been made toward laser-writing techniques and assembling integrated optics, the physical mechanisms underlying glass modifications have not been fully understood. However, further development of laser-writing techniques for controllable generation of desired modifications in transparent materials is impossible without deep understanding of the governing mechanisms of modifications. In this report, we will review the physical processes and mechanisms responsible for various forms of glass modification. Different routes of photoexcitation with creation of dense plasma inside glass bulk will be analyzed depending on the irradiation conditions. Relative contributions of multi-photon and tunneling ionizations and the avalanche process will be considered. The thermodynamic and thermomechanical processes following plasma recombination at different space and time scales will be discussed. A number of intriguing experimental evidences will be canvassed with their detailed theoretical analysis. The results of modeling based on the Maxwell.s equations will be presented for the particular irradiation regimes when different modifications are observed such as nanograting structures and microvoids. The levels of plasma densities and glass matrix temperature distributions upon plasma recombination will be compared and a criterion of glass rupture will be discussed. On the basis of the theory of thermoelastoplastics, we will show that void formation is not obligatory involves the TPa or GPa pressure levels. A special attention will be paid to the collective plasma effects whose role in formation of exotic structures inside and on the surface of transparent materials is highly underestimated. In particular, we will show that the standing waves in confined plasmas can strongly influence the dynamics of laser light absorption. Finally, the most intriguing effects upon laser-induced glass modification which still require explanations and adequate theoretical descriptions will be outlined.