In the last few years, molecular modeling has become a relevant tool for research and teaching purposes in chemistry and molecular biology, allowing the design and development of new molecular structures and materials. In the present chapter, the focus of molecular modeling methodology is addressed towards the mechanistic origin of spiral organization of graphitic materials. A recently proposed catecholporphycene (CPo) model for eumelanin, and both "arm-chair" (A) and "zig-zag" (Z) single layer graphene spirals were chosen as case studies to be analyzed by molecular modeling after MM+, PM3, and extended Hückel geometry optimization using HyperChem v7 software. The poly- CPo eumelanin model corresponds to a highly conjugated graphite-like planar structure based on the polymerization of 5,6-dihydroxy-indole monomers, using all the reactive carbon radicals. Formation of ether bridges between catechol groups of the polymer induces a constrained curvature due to the newly formed furan rings, which in turn results in a spiral organization of poly-CPoe. Interestingly, published molecular modeling studies on graphene properties show a spiral structure, which generates improved opto-electronic properties. However, it is not obvious why a graphene layer should be curved lacking any chemical modification of the original planar polymer. Regarding oxidation, it is tempting to speculate that the possible attack of graphene edges by oxidant agents (e.g., singlet oxygen), could introduce hydroxyls along the reactive A and Z edges, which after ether bridging would result in curved and then spiral graphenes just as it is revealed by molecular modeling. Likewise, in addition to furan, cyclopenta-dienyl and pyrrole rings, oxo and peroxide bridges along graphene edges do result in a spiral structure. In all cases, oligomer stacking generates fused LUMOs at low energies. Stacked poly-CPoe and graphene spirals show compact and very close HOMO (valence band, VB) and LUMO (conduction band, CB) levels, fused LUMOs and strongly reduced energy gap (Eg). It is worth to note the clear similarity between the fused LUMOs of a spiral graphene and the poly-CPoe eumelanin model, which is related to the striking semiconductor characteristics of these amorphous graphitic compounds. Likewise, molecular modeling methods allow the design of new bioinspired materials (e.g., planar and spiral poly-catechol-imidacene) and explain the massive fusion of longitudinal and transversal LUMOs continuum from stacked, intercalated and bilayered graphitic spirals yielding compact and close VB and CB.