The first aim of this project "Superconcentration in random geometric structures" is to investigate the phenomenon of superconcentration for measurable functionals of a Poisson process on an abstract space, specifically, to find some very general conditions under which superconcentration holds. Secondly, our goal is to improve known state of the art methods, such as the second-order Poincaré inequality, to obtain quantitative central limit theorems for Poisson functionals that are superconcentrated. Finally, we aim to exploit the connection of superconcentration to the notion of noise-sensitivity. One of our main goals is to study (sharp) noise-sensitivity in various continuum percolation models by exploring this connection, as well as other avenues based on spectral methods and differential inequalities.