We review the hypothetical interactions predicted beyond the Standard Model which could be constrained by using the results of tabletop laboratory experiments. These interactions are described by the power-type potentials with different powers, Yukawa potential, other spin-independent potentials, and by the spin-dependent potentials of different kinds. In all these cases the current constraints on respective hypothetical interactions are considered which follow from the Casimir effect and some other tabletop physics. The exotic particles and constraints on them are discussed in the context of problems of the quantum vacuum, dark energy, and the cosmological constant.