We address the problem of designing optimal network topologies under arbitrary optimality requirements. Using three critical system parameters, efficiency, robustness and cost, we evolve optimal topologies under different environmental conditions. Two prominent classes of topologies emerge as optimal: (1) Star-like topologies, with high efficiency, high resilience to random failures and low cost, and (2) ¿Circular Skip Lists¿ (CSL), with high robustness to random failures as well as targeted attacks, and high efficiency at moderate cost. We analyze CSLs to observe that they show several structural motifs that are optimal with respect to a variety of metrics.