Abstract: Indirect Reciprocity (IR) – Alice behaves adequately towards Bob; Carol knows about it and thus helps Alice – is a central mechanism to explain human cooperation. IR involves reputation, status and complex information processing, being the most specifically human of all cooperation mechanisms discovered to date. Understanding evolutionary dynamics under IR can shed light on human social behaviors and morality. Simultaneously, IR can inform about ways of engineering cooperation in new one-shot interaction paradigms where reputations are central – such as web-based platforms or, with the advent of Artificial Intelligence, agent-agent and human-agent interactions. In this thesis we develop a formulation of IR to deal with populations of finite size and, in this context, investigate the limits of IR in promoting cooperation along several nonexcluding directions. We start by exploring the stochastic dynamics of IR employing an analytical framework that relies on the assumption that exploration rates – the likelihood of spontaneously adopting another strategy – are low. Subsequently, we develop a computational model to simulate, visualize and investigate the evolutionary dynamics, under IR, of populations of finite size and at arbitrary exploration rates. This allows us to study, originally, the impact of two key features of human social interactions: (i) costly reputation building, whereby individuals may decide to pay a cost to share the outcome of a private interaction; (ii) high order social norms, including the past reputations of individuals (fourth-order under the existing IR hierarchical classification). The complexity of both norms and strategies involved in (ii) called for the development of a new paradigm in assessing information exchange and processing in IR. To this end, we propose a new means of quantifying the complexity of both norms and strategies, resorting to concepts rooted in Boolean algebra. Employing these new methodologies, we conclude that (i) the leading norms capable of promoting cooperation, not only depend sensitively on the population size, but also they may be affected by high exploration rates, which may both improve and harm cooperation, depending on the social norm at work; (ii) under costly reputation building, cooperation depends on the ability of individuals to anticipate accurately the reporting intention of their peers. Finally, we identify a key pattern of fourth-order norms that constitutes a necessary condition for a norm to promote cooperation. We show that, out of 216 possible norms, there exists one very simple norm that complies with this pattern, promoting high levels of cooperation while ignoring the previous reputation of individuals.