The tone and volume
controls

Between the pick-ups and the output jack you will find the tone and volume controls, that regulate both the tones and the output volume of the instrument. The volume control has a capacity meter that modifies the output signal by means of a variable resistor that is connected to the control knob placed on the body of the instrument. This has a resistance, usually in the shape of a horseshoe. An elliptical contact is connected to the post of the knob, so that when the knob itself is turned, the contact changes the resistance. Two wires coming from the pick-ups are connected to either end of the contact: one with zero tension, the other is at the maximum. When moving, the elliptical contact transmits the output tension value of the control.
The tone control also has a post and a control knob on the body of the instrument. The fuction is a combination between a control meter and a condenser. They transmit the high frequencies and discharge them to ground. The high frequencies go to the condenser, which acts as a filter, where the low frequencies don't pass. When turning the knob, the control with its sliding elliptical contact determines how much high frequency must be discharged. With the tone control openned to its maximum, the entire signal generated by the pick-up is sent to the output of the control, while at the minimum the high frequencies are filtered out.
A common error is to think that the open tone meter increases the high frequencies, and closed emphasizes the low frequencies. As we have just seen, the low frequencies created by the pick-up are not touched, while the high frequencies are cut the more the control is closed.

The fixed bridge

On the electric guitar, the bridge is of fundamental importance for many reasons. Like the acoustic instrument, the strings are anchored to the bridge, but there are other factors that increase the technical characteristics of the bridge. There are two types of bridges that can generally be found on the electric guitar: the fixed bridge and the tremolo bridge (also called the vibrato bridge). The fixed bridge consists of a metal plaque screwed to the body on which the adjustable saddles are mounted. These regulate the intonation of the instrument (not to be confused with the tuning), an operation that done by adjusting the saddle in order to register the diapason, which is the active length of the string from the bridge to the capo. Furthermore, the saddle is adjustable in heighth, in order to modify the action of the strings on the fretboard with respect to the curvature of the fretboard itself. There are various fixed bridge models, but we can name for example the Tune-O-Matic by Gibson (used on the Les Paul), or the various models for Fender (used on the Telecaster, the Jaguar, etc).
On semiacoustic instruments you can find a tailpiece bridge, which is a mobile wooden bridge, blocked by the pressure of the strings that are anchored to the tailpiece. The tailpiece is a metal plate with slots where the strings are anchored. The plate is screwed to the side panel.

The tremolo bridge

In the case of the tremolo bridge, there has always been the search to improve the functionality and the intonation. Besides that, the term "tremolo"is not exactly correct, which indicates a "manuale" effect of the fingers on the fretboard of the guitar: the term vibrato is more precise, in fact, this is called the vibrato lever. But lets go in order.
The main function of the tremolo bridge is to vary the intonation of the strings, in an increasing or decreasing manner. This is possible due to the mobile bridge, that is held in a fixed position by springs placed under the bridge itself and anchored to the body of the instrument. A vibrato lever is attached to the bridge: when the right hand puts pressure on the lever, the bridge moves, releasing the tension of the strings. Releasing the lever, the springs bring the entire block back to its origional position. It's also possible to pull the lever, in order to increase the tension of the strings, which return to the correct intonation when the lever is released.
This was the idea that started the experimentation back in the 1950's, thanks to two devices like the Fender tremolo mounted on the Stratocaster, and the Bigsby tremolo, even if this last one uses a slightly different vibrato system (softer but less precise). The problems, are always related to the return phase of the springs, which don't respond well to frantic use of the lever. Until the mid 1960's the lever was seen as a true tremolo effect, but with the continuous evolution and research of sounds and particular effects on the instrument some minor intonation defects were discovered. You just need to think of Jimi Hendrix, surely one of the first to explore new guitar solutions using the tremolo lever. Today many typical sounds derived from the use of the lever are common.
In the 1970's, the search for the perfect intonation brought about the construction of more sophisticated tremolo bridges, such as the Floyd Rose, Shaller, Steimberger and more recently Levinson, Wilkinson and AlecB. As you can see, there are many models, and each has its own construction philosophy. Probably the model imitated the most is the Floyd Rose. The technique that makes it possible to obtain large movements in the tension of the strings, without compromising the intonation once the bridge is in the static phase, is the complete block of the strings on the bridge, thanks to the saddle that tightens the strings on the bridge and to a sting lock situated on the headstock, which doesn't allow the strings to move from the tuners.

As stated before, there are numerous models of bridges. For example, the Steimberger bridge has the job of completely tuning the instrument (the Steimberger doesn't have a headstock, therefore no tuners), an operation that is done by means of a particular system of saddles that slide inside the bridge.
In many cases, the search was to have Fender-style bridges, therefore without string locks, but much more secure on an intonation level, thanks to particular systems of internal springs or plaques (levinson), or even very recent models of the AlecB tremolo bridge, which is based on a balanced movement using ball bearings.
To finish, I would like to remind you of the transpositional bridges, like the Trans-trem by Steimberger, that can "host" different tuners, thanks to a selector on the bridge itself.