Carbon Nanotube Field-Effect Transistors (CNFETs) can revolutionize the design of highly energy-efficient future electronic systems. In the past, carbon nanotubes (CNTs) faced major obstacles such as substantial imperfections and variations inherent to CNTs, and low CNFET current densities. A combination of CNFET circuit design and CNT processing techniques (the "imperfection-immune paradigm") overcomes these challenges to enable the experimental demonstration of the carbon nanotube computer, and, more generally, arbitrary CNFET digital systems. These are the first system-level demonstrations among promising emerging nanotechnologies for high-performance and highly energy-efficient digital systems. We will also discuss new nanosystem architectures enabled by CNFETs. Such architectures are key to achieving very high degrees of energy efficiency for emerging abundant-data applications.