The development of the jet engine in the post war years was based mainly on the need for greater power; in those days, fuel costs were a relatively minor. Latterly, environmental demands (noise and emissions reductions) as well as economy and power demands have become the main reasons development has progressed.
Early Development
Power demands forced ever higher compression ratios, this led to the change from simple centrifugal compressors to axial flow compressors.
Unfortunately, axial flow compressors suffer from a phenomenon called surge; put simply, this where the rear of the compressor cannot get rid of all the air from the front of the compressor. Strange as it may sound, but this usually occurs at the lower rpm range, at the higher rpm’s, the air flow at both ends of the compressor is matched, therefore surge does not usually happen unless a fault or failure occurs.
At the lower rpm’s (or ‘off design’ condition), the front of the compressor (with its large blades) can move more air rearwards than the rear end (with its small blades) can cope with. This means the smooth airflow is disrupted and the excess air can go rapidly forwards, then the airflow restores then goes rearwards again. This happens at a rapid rate and the compressor is said to be surging; the resultant vibration can cause undesirable mechanical failures.
There are numerous ways to get rid of this excess air, or to state more correctly – match the airflows throughout the compressor at the off design condition, such as:

• Open a hole in the side of the compressor i.e. bleed valve.
• Allow the excess air to ‘bypass’ (or go around) the rear of the compressor, and the bypass engine was born.
• Split the compressor to allow the front end to slow down, thereby moving less air, and the rear end to speed up, moving more air.
• Redirect the flow of air at the front of the compressor with ‘Variable Inlet Guide Vanes’ (VIGV’s).

Later Development
In reality, modern engines feature bypasses, multi shafts, VIGV’s (and VSV’s – Variable stator Vanes), and numerous bleed valves, with sophisticated control of variable vanes and the bleed valves, the latter mounted at different stages of the compressor and opening/closing at different rpm values.
Any air passing through the bleed valves is contained within the engine, thereby is not lost in terms of thrust, unlike the early engines such as the Avon, where bleed air was simply ejected overboard through the aircraft fuselage.
Improvements are constantly being sought to reduce fuel consumption, emissions, and noise.

Jet Engine Types – Bypass Engines

The illustration below shows a typical large bypass engine.
Engines are loosely categorised by the size of the bypass compared to the core flow.
The amount of air entering the core engine compared to the bypass duct is called the bypass ratio.
Low Bypass
Low bypass ratio engines tend to be either older designs of civil use engines or modern military engines.
The Rolls-Royce Spey has a bypass ratio of approximately 1:1, (it does vary slightly with the mark of engine). That is all the air entering the engine passes through the LP compressor, then half the air goes through the core or hot section (i.e. the HP compressor, combustor and turbine sections), and the other half goes through the bypass and remixes with the core flow before passing through the propelling nozzle to atmosphere.
These engines are more often than not two shaft engines, with the notable exception of the RB199 in the Tornado, which is a three shaft layout.
Medium Bypass
A bypass ratio of around 5:1 is common. Civil engines such as the BRR715, the IAE V2500 family fall in this category.
High Bypass
High bypass ratio of 10:1or higher, again varying with the engine type/mark.
General
In both the Medium and High bypass ratio engines , all the air entering the engine passes through the LP Fan, then the flows are split between the core and bypass sections of the engine.
The Rolls-Royce RB211 and the Trent family of engines are a three shaft layout, i.e. there is an LP compressor (the Fan), and IP or Intermediate Compressor and the HP compressor, each compressor driven by its own turbine section. I the three shaft layout, the LP system runs at the lowest speed, the HP runs at the highest speed.
Also shown below is a cut-away showing the internals, a view of the same engine in its cowls as it would be fitted to the airframe, and a photograph of the Trent 1000 for the Airbus A380, showing the size of the engine compared to the engineer included in the photograph.
Engines of this size pose the own logistics problems, such as:-
How is the engine transported from the engine production plant to the airframe manufacturers.
How is the engine removed from the airframe for maintenance and overhaul operations.

Jet Engine Types – Vectored Thrust

History
Prior to this engine entering service, numerous experimental aircraft were tried to provide vertical take off and landing (VSTOL). These featured vertically mounted ‘lift’ engines, horizontal engines with fixed downward facing nozzles, and even turbo prop aircraft that stood on their tails or landed on a vertical ramp.
The only practical VSTOL engine was the Rolls-Royce Pegasus series fitted into the Harrier ‘Jump’ Jet,
Rolls-Royce Pegasus
This medium bypass engine is unique in that it can provide vertical thrust for VSTOL operation and forward thrust for normal flight.
The air entering the engine flows through the LP compressor and is then split into the bypass and core flows. The thrust is directed through four vectoring (rotating) nozzles; the two front ‘cold’ nozzles take what would be the bypass flow, and the two rear ‘hot’ nozzle take the core flow.
In addition to the four main nozzles, there are a number of downward pointing ‘puffer’ nozzles at the aircraft extremes, such as the wing tips the nose and the tail. These are used to keep the aircraft in a stable attitude in the hover. The tail puffer also feature a left and right (port and starboard) puffer nozzle to rotate the aircraft again whilst in the hover.
The nozzle position is controlled by the pilot via a dedicated lever in the cockpit. With this control the aircraft is capable of unusual manoeuvres, such as during high speed flight the nozzles can be pointed in a slightly forward position, causing a rapid reduction forward speed.
The engine shaft contra-rotate (rotate in opposite directions), this  is another engine feature which assists in the stability of the aircraft whilst in the hover. This contra-rotation cancels out a phenomenon known as ‘torque reaction’. This is caused in the turbine as the gas stream hits the stators and is redirected onto the turbine blades. An equal and opposite reaction to the gas redirection is to try and push the stators in the opposite direction to the turbine rotor.
Future Aircraft
The Harrier replacement, the JSF (Lockheed Martin F-35), is powered by what effectively a turbo shaft engine. The main engine features a single rear mounted twisting nozzle that either points rearwards or downwards. Additional vertical thrust is provided at the front of the aircraft by an vertically mounted fan, driven by a power offtake shaft from the main engine. As the aircraft goes into vertical thrust mode, the forward mounted fan powers up, and doors open just behind the cockpit on the upper and lower fuselage surface to allow air to be pulled in at the top and ejected as vertical thrust out the bottom.

Jet Engine Types – Turbo Prop Engines

Turbo prop engines extract most of the energy from the gas stream to drive a propeller which provides the thrust, as apposed to providing pure thrust from the engine exhaust.
Some residual thrust is still available at the jet pipe, and in the case of the Rolls Royce Dart engine, this is mathematically converted to Shaft Horse Power, and is known as ‘Equivalent Thrust’.
In the Dart, the turbine drives both the compressor section and the propeller.
The propeller drive passes through a reduction gearbox, which provides a 16:1 reduction in rpm, and an opposite direction of rotation.
The gears within the reduction gearbox also provide an indication of engine power, in the form of an oil pressure, called ‘Torque Pressure’, this is indicated on the flight deck.

Jet Engine Types – Turbo Prop and Shafts

Below is shown a variety of engine layouts, described below
Rolls Royce Allison T56-A-15 Turbo Prop
A four stage turbine drives the 14 stage compressor and the propeller.
The propeller is driven by the engine shaft extending into a separately mounted gear box, therefore the thrust from the propeller is passed through the gearbox casing to the airframe and not through the engine.
Rolls Royce Tyne Turbo Prop
A very successful engine in terms of reliability and economy, which was used in a variety of aircraft.
It features a two shaft layout. The single stage HP turbine drives a 9 stage HP compressor, and the three stage LP turbine drives a six stage LP compressor and the propeller through a reduction gearbox.
Lycoming T55-GA-714
Two of these engines power the Boeing Chinook transport helicopter in service with the RAF.
The engine features a 2 stage HP turbine driving a compressor which has both axial flow at the front and centrifugal flow at the rear. The two stage LP turbine drives the only the output shaft.
This latter feature is known as a ‘free power’ turbine, that is, a turbine which is used for driving an external, propeller, rotor, ships screw or even a pump.
The engine has a reverse flow combustor, where the air from the compressor is turned from a rearward flow into a forward flow through the combustion phase.
This combustor design has minimal effect on power development but considerably reduces the overall length of the engine, and is used where the engine cross section is less important from a drag perspective; the design can also reduce engine weight, as shorter relatively heavy shafts are required.
The drive from both of the Chinook engines is fed into a gearbox known as the Combining Transmission. From this gearbox there is a drive shaft to feed both the forward and rear rotors. Therefore, both rotors turn at the same speed but in opposite directions to prevent rotor blade clash. The rotors are permanently linked, hand turning the front rotor will also turn the rear rotor and vice-versa.
The arrangement also means that if one engine fails, the other can continue to drive both rotors.
General
All of these engines will have some level of residual thrust produced by the hot exhaust flow; this is never wasted and is used to assist in powering the aircraft forward.