The classical Noether's Theorem yields conservation laws (CLs) arising from continuous symmetries of functionals whose extrema solve the corresponding Euler-Lagrange equations. After reviewing Noether's Theorem and its severe limitations, we present the Direct Construction Method (DCM) to find directly the CLs for any given system of differential equations. The DCM yields the factors for CLs as well as an integral formula for corresponding conserved densities. The factors are symmetries of the given system of differential equations if and only if the given system has a variational principle. The action of a symmetry (discrete or continuous) on a conservation law yields CLs. Conservation laws of a given system of differential equations yield non-locally related systems that, in turn, yield algorithms to obtain nonlocal symmetries (and nonlocal CLs as well as extensions of qualitative, numerical and perturbation methods) for a given system. Moreover, from its admitted symmetries or factors for conservation laws, one can determine whether or not a given system of PDEs can be linearized by an invertible transformation and find its linearization when it exists. All of these connections are algorithmic. Examples will be given and some open problems will be presented.