We present a new class of conservative method, called the multiplier method, which enables systematic construction of conservative schemes for general dynamical systems. Specifically, the multiplier method can preserve arbitrary forms of conserved quantities and is applicable for systems without a symplectic or variational structure, such as dissipative problems. Moreover, we discuss a fundamental long-term stability property for general conservative methods. This is joint work with Alexander Bihlo and Jean-Christophe Nave.