I describe Extremal Optimization (EO), a general-purpose, local search heuristic for hard combinatorial (and physical) problems  such as bi-partitioning (ie, model-B ferromagnets), coloring (ie, Potts antiferromagnets), and max-cut (ie, Ising Spin Glasses). EO is motivated by the Bak-Sneppen model of self-organized criticality (SOC). SOC provides a general dynamics of driven dissipative systems that operate far from equilibrium and exhibit many emergent properties,  such as scale-free fluctuations, memory and learning, and persistent returns to untypical (here: ground-state) configurations. The generic properties of EO are explored, which explain the efficiency of EO in searching many 'complex energy-landscapes'. Numerical results of EO are discussed especially for the Edwards-Anderson spin-glass problem.