* Largest by physical size: This would likely be one of the massive motors used in industrial applications, such as those found in some ship propulsion systems or large power plants. These can be tens of meters long and weigh hundreds of tons. Precisely identifying the absolute largest is difficult due to proprietary information and constant advancements.
* Highest power output: Again, this is difficult to pinpoint. Large generators in power plants are incredibly powerful, but they are generators, not motors *per se*. Very large electric motors used in industrial applications or specialized applications like mining or ship propulsion systems continually push the boundaries of power output.
* Highest torque: Similarly, motors designed for extremely high torque applications (like massive conveyor belts or extremely slow-speed, high-load machinery) would compete for this title.
In short, there's no single "biggest" motor. The title depends on your definition of "biggest," and the information on the largest motors in each category is often not publicly available.