The growth-fragmentation equation (GFE) is a model which describes the evolution over time of a population which grows and divides, with respect to a structuring variable. This PDE appears in many applications such as: crushing rocks, combustion, which are pure fragmentation phenomena, and also: cell division, protein polymerization, data transmission protocols, neurons networks. After presenting the theory which has been developed during the last decade, we will focus on two questions. From a noisy measurement of the solution in large time how the division rate can be estimated? This problem has some interesting applications in cell biology. The second question will be: Is there a decay to a steady state for a non linear GFE used in neuroscience?