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This article introduces a new approach for conflict resolution: given a set of tuples pertaining to the same entity, it identifies a single tuple in which each attribute has the latest and consistent value in the set. This problem is important in data integration, data cleaning, and query answering. It is, however, challenging since in practice, reliable time stamps are often absent, among other things. We propose a model for conflict resolution by specifying data currency in terms of partial currency orders and currency constraints and by enforcing data consistency with constant conditional functional dependencies. We show that identifying data currency orders helps us repair inconsistent data, and vice versa. We investigate a number of fundamental problems associated with conflict resolution and establish their complexity. In addition, we introduce a framework and develop algorithms for conflict resolution by integrating data currency and consistency inferences into a single process and by interacting with users. We experimentally verify the accuracy and efficiency of our methods using real-life and synthetic data.