Although wireless information theory has been declared dead many times over, the field today is thriving with abundant open problems of significant theoretical and practical importance. This talk will explore our results on wireless information theory that go towards infinity in some dimensions, and back from infinity in others. In particular, we will describe our work on achievable rate regions for single-hop networks with any number of users, obtained through user virtualization followed by coding via a graphical Markov model.  The resulting achievable rate regions meet or exceed all existing rate regions for any single-hop network, including those of interference channels, broadcast channels, and cognitive radio channels. We will also explore the capacity of massive multiple-antenna (MIMO) systems in both the narrowband and wideband regimes, demonstrating that, in some cases, non-coherent communication has no capacity loss compared to coherent communication. Moving back from infinity, we examine the implications on channel capacity and rate distortion of finite delay, energy, and sampling rate. We will particularly focus on our results unifying sampling and rate-distortion theory, where we demonstrate that minimal reconstruction distortion for analog-to-digital converters is achieved with sub-Nyquist sampling when the output bit rate is constrained. We end the talk describing additional dreams and challenges in wireless information theory, including the application of information-theoretic analysis tools to explore new frontiers in biology and neuroscience.