  Irreducible symplectic varieties are higher-dimensional analogues of K3
surfaces. In this paper, we prove the finiteness of twists of irreducible
symplectic varieties via a fixed finite field extension of characteristic $0$.
The main ingredient of the proof is the cone conjecture for irreducible
symplectic varieties, which was proved by Markman and Amerik--Verbitsky. As
byproducts, we also discuss the cone conjecture over non-closed fields by
Bright--Logan--van Luijk's method. We also give an application to the
finiteness of derived equivalent twists. Moreover, we discuss the case of K3
surfaces or Enriques surfaces over fields of positive characteristic.
