Although `quantum contextuality' is one of the most fundamental non-classical features, its generic role in information processing and computation is an open quest. This talk provides a summary of the main results presented in two articles [PRA 100, 022108 NJP 21, 093057]. In a nutshell, these results establish significant interconnections between quantum communication and quantum contextuality, providing deeper insight into the origin of quantum communication advantages. We consider a class of communication tasks, namely, oblivious communication (OC) tasks. The communication in these tasks is constrained such that the receiver remains oblivious to certain information held by the sender. It is first pointed out that any advantage in this task over the classical channel signifies preparation contextuality. One of the predominant manifestations of quantum communication advantage is captured in communication complexity (CC). We show that this widely studied quantum communication complexity advantage implies advantage in oblivious communication, thereby revealing preparation contextuality. Along with this, we introduce a family of CC and OC tasks based on logical proofs of Kochen-Specker (KS) contextuality and show that quantum communication comprised of every KS set of vectors outperforms classical communication.