  Constraints on the Yukawa-type corrections to Newton's gravitational law and
on the coupling constant of axionlike particles to nucleons obtained from
different laboratory experiments are reviewed and compared. The constraints on
non-Newtonian gravity under discussion cover the wide interaction range from
nanometers to millimeters and follow from the experiments on neutron
scattering, measuring the Casimir force and Cavendish-type experiments. The
constraints on the axion-to-nucleon coupling constant following from the
magnetometer measurements, Cavendish-type experiments, Casimir physics, and
experiments with beams of molecular hydrogen are considered which refer to the
region of axion masses from $10^{-10}$ eV to 200 eV. Particular attention is
given to the recent constraints obtained from measuring the Casimir force at
nanometer separation distance between the test bodies. Several proposed
experiments focused on constraining the non-Newtonian gravity, axionlike
particles and other hypothetical weakly interacting particles, such as
chameleons and symmetrons, are discussed.
