Cellular networks have preserved an application agnostic and base station (BS) centric architecture1 for decades. Network functionalities (e.g. user association) are decided and performed regardless of the underlying application (e.g. automation, tactile Internet, online gaming, multimedia). Such an ossified architecture imposes several hurdles against achieving the ambitious metrics of next generation cellular systems. This article first highlights the features and drawbacks of such architectural ossification. Then the article proposes a virtualized and cognitive network architecture, wherein network functionalities are implemented via software instances in the cloud, and the underlying architecture can adapt to the application of interest as well as to changes in channels and traffic conditions. The adaptation is done in terms of the network topology by manipulating connectivities and steering traffic via different paths, so as to attain the applications' requirements and network design objectives. The article presents cognitive strategies to implement some of the classical network functionalities, along with their related implementation challenges. The article further presents a case study illustrating the performance improvement of the proposed architecture as compared to conventional cellular networks, both in terms of outage probability and handover rate.