Devices in a cognitive radio network use advanced radios to identify pockets of usable spectrum in a crowded band and make them available to higher layers of the network stack. A core challenge in designing algorithms for this model is that different devices might have different views of the network. In this paper, we study two problems for this setting that are well-motivated but not yet wellunderstood: local broadcast and data aggregation.We consider a single hop cognitive radio network with n nodes that each has access to c channels. We assume each pair of nodes overlaps on at least 1 ≤ k ≤ c channels.We first describe and analyze COGCAST, a randomized algorithm that solves local broadcast in O((c/k) · max{1, c/n} · lg n) time, with high probability, by spreading information in an epidemic manner through the network.We then propose COGCOMP, a randomized algorithm that solves data aggregation in O((c/k) · max{1, c/n} · lg n + n) time, with high probability. The COGCOMP algorithm uses COGCAST as a key primitive to establish a spanning tree among the nodes, so that data can be aggregated from leaves to root.We conclude with a collection of lower bounds that show COG-CAST is near optimal (in particular, within a lg n factor) in many cases. These bounds introduce new techniques of potential standalone interest for those concerned with proving fundamental limits in the cognitive radio network setting.