We developed a detailed numerical model for GRB prompt emission. For a given relativistic ejection by the central source, we are able to compute the properties of the internal shock phase of the relativistic jet. This dynamical model is coupled to a radiative code to compute the non- thermal emission of each emitting region. Taking into account relativistic and cosmological effects, the synthetic GRB can be computed. I will present a comprehensive set of simulations of GRB spectral evolution and the impact of model parameters related to shock physics and to the initial conditions in the ejecta. In the second part of my talk, I will present the results of the INTEGRAL IBIS/SPI GRB data analysis. The properties of INTEGRAL GRBs are compared with the BATSE and Fermi samples. INTEGRAL IBIS data allow the investigation of the GRB emission on long time scales before and after the main event. I will present the results of the late emission search using the IBIS GRB data.