This paper surveys some new results on digital phase-locked loops (DPLLs) in relation to their well-established theory. The review includes, the non-uniform sampling loop of first order stability in relation to the dynamical system theory and chaos, new details of threshold performance, the chaotic hang up phenomenon in the loop of second order, the local stability of uniform sampling DPLL by Volterra equation in discrete time, the new stability criteria for the non-uniform sampling DPLLs, the loop with sequential filters having a link with the stochastic resonance phenomenon and other refinements in the field.