Analytic computation of multi-loop Feynman integrals is crucial for the current era of precision physics. These analytic computations often bring us to intriguing algebraic structures which helps in establishing deep connections with Mathematics. In this talk, I will present a selected list of multi-loop Feynman integrals with details about their analytic structure. I will also highlight how the analytic complexity changes with a change in the number of loops and legs as well as modern techniques for overcoming these challenges.