We study the design of optimal interventions in network games, where individuals' incentives to act are affected by their network neighbors' actions. A planner shapes individuals' incentives, seeking to maximize the group's welfare. We characterize how the planner's intervention depends on the network structure. A key tool is the decomposition of any possible intervention into principal components, which are determined by diagonalizing the adjacency matrix of interactions. There is a close connection between the strategic structure of the game and the emphasis of the optimal intervention on various principal components: In games of strategic complements (substitutes), interventions place more weight on the top (bottom) principal components. For large budgets, optimal interventions are simple - targeting a single principal component.