Local conservation laws of a system of differential equations are given by one or several expressions of the form divergence(flux vector)=0, holding on solutions of that system. For ordinary differential equations (ODE), conservation laws lead to first integrals and the reduction of order; for partial differential equations (PDE), they are used for analysis of solution behaviour, and provide globally conserved quantities, such as energy, momentum, etc., as well as more exotic ones. Conservation laws also play an important role in the numerical treatment of nonlinear PDE models. In this talk, we will review the general theory, including trivial and equivalent conservation laws, the characteristic form of conservation laws, their relationship with symmetries of DEs, variational systems, Lagrangians, and the first and second Noether's theorems. A systematic general procedure to seek conservation laws will be discussed, applicable to virtually any model; it will be compared to the Noether's theorem approach for variational models. A symbolic implementation of the direct method of conservation law computation in Maple will be discussed. Examples of conservation laws and conserved quantities for classical PDEs and some nonlinear models arising in contemporary work will be presented. Time permitting, we will consider a common framework for different types of conservation laws of PDE systems in three space dimensions, including their global and local formulations in static and moving domains given by volumes, surfaces, and curves.