Question: When working with electronics, it is quite easy to regulate current with a resistor, potentiometer, switcher, etc.

But take a simple high power application such as an electric stove. What method is used to control the current through the burners. They couldn't possibly use a variable resistor because the heat generated would be on par with the burner. 

It is clear however that the controls are disipating very little heat and they certainly aren't using any electronic devices. So how do they do it?

Answer: 
simple electric ovens use simple temperature control usually using something like a bimetallic strip (you can here them click in and out) where the dial is used to set the point of electrical contact that will then provide electrical power to the heating elements.

the result is more of a hysteric control with a very long duty cycle (where the duty is governed by the thermal characteristics of the oven - ie how long to cool) and the lower band to-do with specific characteristics of the thermistor/bimetalic strip.

More modern electronic controllers do a similar thing but use thermalcouples/RTD to measure the temp and then semiconductors to switch the power (SCR's)
Electric ovens and Stove top burners regulate the heat by turning the heating element on or off using a Relay. In my house if you listen closely you can hear the relay on the circuit board click on and off. Again the typical household electric stove heating elements are either on or off.

In larger applications a Thyrister or SCR is used and to pulse the heating element on and off. The SCR can only turn On and Off but can do this very quickly resulting in a short pulse averaging out to be a small current and a longer pulse being a larger current. 

To really see what is happening in a SCR circuit you need an oscilloscope to see the pulses. Any current meter on a circuit such as this will probably give you a RMS current value over time.