Progress in constraining axion and non-Newtonian gravity from the Casimir effect

We consider recent progress in constraining the axion-nucleon coupling constants and the Yukawa-type corrections to Newtonian gravity from experiments on measuring the Casimir interaction. After a brief review of previously obtained constraints, we concentrate on the new Casimir-less experiment, which allows to strengthen the known results up to factors of 60 and 1000 for the axion-like particles and Yukawa-type corrections, respectively. We also discuss possibilities allowing to further strengthen the constraints on axion-nucleon coupling constants, and propose a new experiment aiming to achieve this goal.