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Age of information (AoI) is gaining attention as a valuable performance metric for many IoT systems, in which a large number of devices report time-stamped updates to a central gateway. This is the case, for instance, of remote sensing, monitoring, or tracking, with broad applications in the industrial, vehicular, and environmental domain. In these settings, AoI provides insights that are complementary to those offered by throughput or latency, capturing the ability of the system to maintain an up-to-date view of the status of each transmitting device. From this standpoint, while a good understanding of the metric has been reached for point-to-point links, relatively little attention has been devoted to the impact that link layer solutions employed in IoT systems may have on AoI. In particular, no result is available for modern random access protocols, which have recently emerged as promising solutions to support massive machine-type communications. To start addressing this gap we provide in this paper the first study of the AoI of a scheme in this family, namely irregular repetition slotted ALOHA (IRSA). By means of a Markovian analysis, we track the AoI evolution at the gateway, prove that the process is ergodic, and derive a compact closed form expression for its stationary distribution. Leaning on this, we compute exact formulations for the average AoI and the age violation probability. The study reveals non-trivial design trade-offs for IRSA and highlights the key role played by the protocol operating frame size. Moreover, a comparison with the performance of a simpler slotted ALOHA strategy highlights a remarkable potential for modern random access schemes in terms of information freshness.