Corrections to Newton's gravitational law inspired by extra dimensional physics and by the exchange of light and massless elementary particles between the atoms of two macrobodies are considered. These corrections can be described by the potentials of Yukawa-type and by the power-type potentials with different powers. The strongest up to date constraints on the corrections to Newton's gravitational law are reviewed following from the Eötvos- and Cavendish-type experiments and also from the measurements of the Casimir and van derWaals force.

New experiments are discussed on measuring the Casimir force between metallic surfaces. One of them uses torsion pendulum and the other one - atomic force microscope. The claimed agreement of experimental data with a theory is analyzed. A 5% level of agreement obtained with a torsion pendulum is shown to be in contradiction with the values of surface roughness, finite conductivity and temperature corrections to the Casimir force. A 1% agreement (at the closest separations) obtained with an atomic force microscope is confirmed by the use of more exact theory taking into account higher order surface roughness and conductivity corrections.