We present a semiclassical study of discrete quantum mechanical Hamiltonians using continuous Semi-Classical Initial Value Representation (SC-IVR) methods. This is accomplished using a generalized "Mapping" algorithm that is based on the representation of the quantum number by a continuous action variable that extends from −∞ to ∞. We demonstrate the procedure in a Herman Kluk IVR (HK-IVR) study of non-adiabatic dynamics in a model avoided crossing system. The algorithm can also be systematically extended to give an accurate representation of the dynamical behavior of a quantum system characterized by non-cartesian degrees of freedom. We present a HK-IVR treatment of such a system, comprising a linear rotor molecule in static electric and pulsed laser field. The mapping procedure is shown to make accurate predictions about the dynamical behavior of such non-cartesian systems. Finally, we present an analysis of the recently developed Semi-Classical Coherent State Path Integral (SC-CSPI) propagator. The numerical implementation of the propagator involves a "root" search problem in "complex" phase space, typically achieved via the Newton-Raphson technique. In our application of the method studying the absorption spectra of Iodine, we demonstrate the superior numerical efficiency of the SC-CSPI propagator as compared to contemporary IVR techniques. We further demonstrate that the "roots" or "branches" are intimately connected with the recurrences of classical motion in the system, each "branch" being characteristic of a particular recurrence. Unfortunately, finding these classical recurrences or their corresponding "branches" in multidimensions is a prohibitively difficult task. We propose an alternative root search procedure to tackle this problem, where one gradually builds up the solution by perturbatively tuning the parameters characterizing the system. The procedure is demonstrated for a chain of six anharmonic oscillators with harmonic nearest neighbor coupling. This system has been known to exhibit the formation of "localized" vibrational modes known as "discrete breathers". Using the "perturbative" root search procedure we build up these breather modes by slowly varying the intersite coupling. Our results suggest that the SC-CSPI propagator may serve well as a viable alternative to SC-IVR methods.