New design paradigms for insensitive high explosives are being sought for use in munitions applications that require enhanced safety, reliability and performance. We describe recent work of our group that uses an integrated approach to develop predictive models, guided by experiments. Insensitive explosive can have relatively longer detonation reaction zones and slower reaction rates than their sensitive counterparts. We employ reactive flow models that are constrained by detonation shock dynamics (DSD) to pose candidate predictive models. We discuss the variation of the pressure dependent reaction rate exponent and reaction order on the length of the supporting reaction zone, the detonation velocity curvature relation, the computed critical energy required for initiation, the relation between the diameter effect curve and the corresponding normal detonation velocity curvature relation.