This dissertation theoretically analyzes how networks of relationships among decision-makers affect two kinds of economic processes: (i) investment in public goods; and (ii) repeated updating of beliefs or behaviors based on observing neighbors. The results connect these processes to the spectral properties of networks -- that is, eigenvalues and eigenvectors -- and use the connection to shed light on economic outcomes. The first essay, based on joint work with Matthew Elliott, focuses on games in which each player simultaneously exerts costly effort that provides different benefits to each other player. The goal is to find and describe effort profiles that are immune to coordinated coalitional deviations when such a game is played repeatedly. Formally, these effort profiles are the ones that can be sustained in a strong Nash equilibrium of the repeated game. We introduce a class of effort profiles that are called centrality-stable. These are characterized by a network centrality condition: agent A's contribution (defined as effort level times marginal cost) is equal to a weighted sum of the contributions of those who help A; the weight on B's contribution measures the marginal benefit B's effort provides to A. Under certain assumptions (mainly concavity of utility functions), centrality-stable profiles exist, are Pareto-efficient, and any such profile is sustainable in a coalitionally robust equilibrium of the repeated game. Centrality-stable profiles also have an alternative definition: they are those at which all agents are first-order indifferent to scaling all efforts by a factor near $1$. This single condition rules out all profitable coalitional deviations. The results are obtained without parametric assumptions, using the theory of general equilibrium and its relation to the core, along with the Perron-Frobenius spectral theory of nonnegative matrices. When agents are uncertain about each other's utility functions but can verify marginal costs and benefits at an implemented effort profile, then the centrality-stable profiles are the only ones that are immune to manipulation through misreporting of preferences. The second essay, based on joint work with Matthew O. Jackson, studies learning in a setting where agents receive independent noisy signals about the true value of a variable and then communicate in a network. They naively update beliefs by repeatedly taking weighted averages of neighbors' opinions. We show that all opinions in a large society converge to the truth if and only if the influence of the most influential agent on the long-run beliefs vanishes as the society grows. We also identify obstructions to this, including the existence of prominent groups, and provide structural conditions on the network ensuring efficient learning. The third essay, also based on joint work with Matthew O. Jackson, examines how the speed of such an updating process depends on homophily: the tendency of agents to associate disproportionately with those having similar traits. When agents' beliefs or behaviors are developed by averaging what they see among their neighbors -- as in the learning model discussed above or in a myopic best-reply dynamic -- convergence to a consensus is slowed by the presence of homophily, but is not influenced by network density. This is in stark contrast to the viral spread of a belief or behavior along shortest paths -- a process whose speed is increasing in network density but does not depend on homophily. In deriving these results, we propose a new, general spectral measure of homophily based on the relative frequencies of interactions among different groups.