While the deployment of 5G cellular systems will continue well in to the next decade, much interest is already being generated towards technologies that will underlie its successor, 6G. Undeniably, 5G will have transformative impact on the way we live and communicate, yet, it is still far away from supporting the Internet-of-Everything (IoE), where upwards of a million devices per $\textrm{km}^3$ (both terrestrial and aerial) will require ubiquitous, reliable, low-latency connectivity. This article looks at some of the fundamental problems that pertain to key physical layer enablers for 6G. This includes highlighting challenges related to intelligent reflecting surfaces, cell-free massive MIMO and THz communications. Our analysis covers theoretical modeling challenges, hardware implementation issues and scalability among others. The article concludes by delineating the critical role of signal processing in the new era for wireless communications.