Supercell thunderstorm
The supercell thunderstorm is the biggest, baddest and strongest thunderstorm of them all. Many people have heard of them because they can produce tornadoes and are responsible for the hundreds of tornadoes - some of them strong and violent, that strike Tornado Alley each year. They generally produce the most severe weather, such as hail (golf-ball sized or larger) torrential rain, violent straight-line winds, frequent and damaging lightning and of course tornadoes. Out of all thunderstorms, these are the rarest, and of all supercells only a tiny percentage actually produce tornadoes. 
A supercell storm is defined as a thunderstorm with a deep rotating updraft called a mesocyclone. In order for a mesocyclone to develop, supercells must exist in an environment with strong speed and directional wind shear. Supercells also need a large amount of instability (CAPE), although they can occur in low-CAPE environments. As such, they tend to form in the midlatitudes from spring - autumn, when CAPE and shear values are both high enough to sustain a mesocyclone. They don't occur in the tropical regions because there is rarely enough wind shear here (winds remain slack throughout the atmosphere). Supercells are most common in the spring across the central USA, when moderate to strong wind shear and CAPE are both present. Supercells also occur in Europe, although the small landmass, as always, limits the potential for storm development in the UK, where they are a rare visitor. Supercells can form in the UK at any time of the year, although they are most common in the summer, when more significant instability is available due to solar heating. 
     There are three main variations of the supercell thunderstorm:
  • Classic
  • High precipitation (HP)
  • Low precipitation (LP) 
These three types pretty much mean exactly what they say: HP supercells produce copious amounts of precipitation that may envelop and hide any tornado that does form. LP supercells, like the one below, have a mostly rain-free base allowing the storm structure and any tornado to be clearly visible, although they are generally the least likely to produce a tornado. Classic supercells tend to be a mixture of both. 

Image of a classic/ LP supercell that I witnessed whilst stormchasing in the Texas Panhandle on the 22nd April 2015. This storm produced two weak tornadoes and multiple funnel clouds over open countryside - made all the more spectacular since it was backlit by the setting sun! 
A spectacular panoramic image of the mesocyclone of a supercell. You can tell the cloud in the centre of the image is rotating because of the horizontal striations around it. The lowest cloud to the ground is called the wall cloud, and it is from this that a tornado may form. The wall cloud may only be a few hundred metres above the surface, and is an area of further enhanced rotation. At the top of the picture, precipitation is forming in the main updraft and falling on the right of the image. 
Supercell thunderstorms are very large thunderstorms, with one principle updraft. They are able to grow very large because the wind shear separates the updraft and downdraft so that they do not intefere with one another (see section on how single cell storms decay). As a result, a persistent updraft and downdraft both develop and the storm will have a lifetime of several hours - some may last for 6 hours or longer. They only weaken if solar insolation weakens (it becomes night), depriving the storm of warm, moist air close to the surface, or if one moves into an area with low wind shear so that the downdraft begins to obstruct the updraft (unlikely to happen). The process that makes a supercell spin is discussed in the section 
role of wind shear in thunderstorm development.
Above is a schematic and a simple radar depiction of a classic supercell. This type generally has lower radar reflectivities and the updraft is often rain free. In the radar echo, the "hook" at the bottom of the storm is caused by rain and falling precipitation getting wrapped around the mesocyclone and falling at the rear of the storm. This is known as the rear flank downdraft, and can be the sting in the tail of a passing supercell. 
From Markowski and Richardson textbook: Mesoscale Meteorology in Midlatitudes, 2010). 
The tornado generally forms from the lowering and rapidly spinning wall cloud and is located at the rear of a supercell. In the top image above, the tornado would be located in the updraft region at its intersecion with the hook. This is also at the intersection between the mini cold and stationary fronts in the diagram. These are "fronts" in the mesoscale sense: the cold front is generated when the cool rear flank downdraft air gets wrapped all the way around the hook echo and moves in the direction of storm motion. The stationary front is the boundary between the cool forward flank downdraft air and the warm, moist air that will eventually ascend into the updraft. Often, when a supercell has a tornado that is on the ground, the hook echo becomes much more pronounced on radar imagery, as the precipitation gets wrapped around the more rapidly rotating updraft, wall cloud and sometimes the tornado itself. This is not always the case: some supercells may produce a tornado with little or no hook echo: others may have a well defined hook echo but no tornado (albeit a very strong circulation, probably). 
Radar reflectivity images of three separate tornadic supercells that produced high-end (F5, F4 and EF-5 respectively) tornadoes that struck the town of Moore, Oklahoma. The tornados are much more obvious here, with pronounced hook echoes in each case. In fact, in each case, right at the tip of the hook, there is an increase in reflecitivty due to debris being lifted into the air as the tornadoes rip up everything in their path. This is indicitive of a very strong tornado. 
Credit: NOAA.
In the UK, most supercells only show weak rotation signitures and don't usually produce a hook echo or a tornado. However, the case of the 28th June 2012 is a rare exception when several supercells developed, spawning an EF-2 and an EF-0 tornado. A radar image of two supercells over the Midlands from that day looked like this: 
Two supercells that developed, with pronounced hook echoes. Here, the black lines represent imaginary cold and stationary fronts as in the schematic of a supercell from above. Supercell thunderstorms like this are exceptionally rare in the UK, however. 
Credit: Netweather.