There are several good answers and relevant comments already.
I'll address a possibly ambiguous point.

You said - "Do all autofocus cameras need motors to drive the lens?"
Others have explained that a "Light field" or Plenoptic camera (Wikipedia) does not need to move the lens at all to alter focus, so does not need focus motors as nothing moves.

However, you also said " ... I would have thought today's modern electronics rendered motors obsolete."
You may have meant that perhaps some thing other than a motor may be used to move the lens elements in some modern cameras.
Loosely speaking, anything that provides mechanical movement can be regarded as being a motor. By that definition, if anything moves mechanically then a motor must be involved.

However, there are various means by which movement can be achieved with a "motor" that is different or very different from traditional ones. Not all of these are (yet) used in camera lenses.

A common motor which is included inside lenses is the SSM or USM = Supersonic Motor or Ultrasonic motor.This Wikipedia article gives a good description. An ultrasonic motor is often a subset of piezoelectric motors which use electrical constriction or expansion of a crystal ti impart movement. Wikipedia noites -

• An ultrasonic motor is a type of electric motor powered by the ultrasonic vibration of a component, the stator, placed against another component, the rotor or slider depending on the scheme of operation (rotation or linear translation).

  Ultrasonic motors differ from piezoelectric actuators in several ways, though both typically use some form of piezoelectric material, most often lead zirconate titanate and occasionally lithium niobate or other single-crystal materials.

  The most obvious difference is the use of resonance to amplify the vibration of the stator in contact with the rotor in ultrasonic motors. Ultrasonic motors also offer arbitrarily large rotation or sliding distances, while piezoelectric actuators are limited by the static strain that may be induced in the piezoelectric element.

It is not essential to use piezoelectric action to produce an SSM / USM but this is usual.

Animated demonstration of SSM / USM

Superb short flash animations of piezo actuators in action .
This is the Minolta CCD antishake piezo actuator system at work rather than focus drive but demoinstrates the basic principals superbly.

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Related patents here and here