The theory of one- and two-photon dissociation processes with strong laser pulses for slowly varying multiple continua ("direct" dissociation) is developed. Closed form expressions for the state preparation and evolution during and after the excitation pulse are derived. We show how saturation of the photodissociation process as a function of the laser power sets in. We also show that for direct dissociation, the fragment state distribution is independent of the laser power. The dependence of spontaneous emission during dissociation (continuum Raman and resonance fluorescence) on the pulse intensity is studied. The formulation is extended to treating resonantly enhanced two-photon dissociation with strong laser pulses. Closed-form expressions for slowly varying pulses and slowly varying continua are derived. Using these expressions, the existence of adiabatic passage to the continuum (APC) by which a system executes a complete population transfer from an initial bound state to the continuum by following two guiding light pulses is established. A simple iterative scheme for going beyond the adiabatic approximation is introduced.