The following situation arises in modeling: one has a system of differential equations with parameters and wants to determine the values of these parameters measuring unknown functions (assuming that perfect noise-free measurements are possible). Usually, some of the unknown functions are impossible or very hard to measure, so only a subset of them is available for measurement. The property of parameters to be uniquely recoverable from measuring a subset of the unknown functions is called structural global identifiability. Several approaches were suggested during last three decades for solving this problem. In this talk, I will describe recent theoretical results in this area and new efficient algorithms. This is joint work with Hoon Hong, Alexey Ovchinnikov, and Chee Yap.