Brushless vs Brushed
Brushless motors essentially invert the design of brushed motors. A motor "brush" is usually mounted in a rotating shaft and it does the work of completing an electrical circuit between stationary parts and moving parts. Brushless motors mount permanent magnets, and rotating electromagnets are attached to the armature. This is only possible because of solid state circuitry (i.e. as in computer chips), which drastically reduces the number of moving parts in a motor.
Stepping
A stepping motor divides a one full rotation into multiple steps, which makes it ideal for precision applications and very slight movements. Stepper motors have saw-shaped electromagnets that are positioned around a toothed rotor. A microcontroller powers each electromagnet to "step" a partial rotation in the direction of that magnet, resulting in incredibly minute control.
Limitations
Brushless motors are limited by what current technology allows in the microcircuitry manufacturing process and the power constraints those imply. So long as microcircuitry can be shrunk, brushless motors can be made in very small configurations.
Advantages
The biggest advantage is the reduction of moving parts, particularly that of removing brushes, which eventually wear down and have to be replaced, which can be very inconvenient for small, embedded parts. Brushless motors are also computer controlled and powered, meaning that they can spin much faster than mechanical brush motors with less heat and wear.