Poincaréinequality is a functional inequality bounding variance by energy with numerous applications: long time behaviour of the associated Markov process, concentration of measure properties... It is thus crucial to get good if not optimal constants in this inequality. We will review various techniques allowing to do so, including Lyapunov method or the famous Bakry-Emery criterion relying on curvature bounds, as well as perturbation "àla" Holley-Stroock. We will then present recent results allowing to refine the Bakry-Emery approach under variable curvature bounds, and also to generalize the perturbation approach.Joint work with P. Cattiaux and M. Fathi.