Despite the hype about blockchains and distributed ledgers, no formal abstraction of these objects has been proposed. To face this issue, in this paper we provide a proper formulation of a distributed ledger object. In brief, we define a ledger object as a sequence of records, and we provide the operations and the properties that such an object should support. Implementation of a ledger object on top of multiple (possibly geographically dispersed) computing devices gives rise to the distributed ledger object. In contrast to the centralized object, distribution allows operations to be applied concurrently on the ledger, introducing challenges on the consistency of the ledger in each participant. We provide the definitions of three well known consistency guarantees in terms of the operations supported by the ledger object: (1) atomic consistency (linearizability), (2) sequential consistency, and (3) eventual consistency. We then provide implementations of distributed ledgers on asynchronous message passing crash-prone systems using an Atomic Broadcast service, and show that they provide eventual, sequential or atomic consistency semantics. We conclude with a variation of the ledger - the validated ledger - which requires that each record in the ledger satisfies a particular validation rule.