The computing world is witnessing a proverbial Cambrian explosion of emerging paradigms propelled by applications such as Artificial Intelligence, Big Data, and Cybersecurity. The recent advances in technology to store digital data inside a DNA strand, manipulate quantum bits (qubits), perform logical operations with photons, and perform computations inside memory systems are ushering in the era of emerging paradigms of DNA computing, quantum computing, optical computing, and in-memory computing. In an orthogonal direction, research on interconnect design using advanced electro-optic, wireless, and microfluidic technologies has shown promising solutions to the architectural limitations of traditional von-Neumann computers. In this article, experts present their comments on the role of interconnects in the emerging computing paradigms and discuss the potential use of chiplet-based architectures for the heterogeneous integration of such technologies.