Think about this for a second: have you ever owned a Tube Screamer? If not, then how many of your guitar-playing friends have? Why does it seem like everyone you know that plays guitar has owned one of these at some point? Let's dive into its history and figure that out.
One of the Most Copied Pedals of All Time
The Ibanez Tube Screamer is arguably one of the most popular guitar effects pedals ever made. A quick google search will show that for every "Top 10" list of effects pedals, it's usually included. 
Sure, pedals like the Boss DS-1, Electro Harmonix Big Muff, Crybaby Wah pedal, and the MXR Phase 90 are popular, but are any of them as recognizable as the Tube Screamer? And for that matter, is there any pedal's circuit that has been copied more than the Tube Screamer? It really isn't that surprising that it's often referred to as the "most copied pedal" of all time. Even if you've never owned a Tube Screamer, there's a good chance that one of your current overdrive pedals is just a glorified rip-off of the TS9.
So what are the ingredients in a Tube Screamer that so many pedals copy? Well, first take light-to-medium overdrive and add electronic field-effect (FET) bypass switching. Next mix it with transistor buffers at both the input and output and bake it with a IC chip that produces symmetrical clipping of the input waveform. If you have a boutique pedal using these ingredients, then you're using a Tube Screamer clone.
One of the earliest Tube Screamer clones. (Reader submission from John G.)
It's worth pointing out that quality components often make the biggest difference between a great-sounding pedal, and a bad one. That is especially true when buying a vintage Tube Screamer, or when buying a newer 808 clone. 
Could you make your own Tube Screamer clone with this schematic?
The First Integrated Circuit Chip
The Tube Screamer first appeared in 1979 in the form of the now highly sought-after and collectible TS808 model. All other overdrives built prior to this model were built around transistors. The 808 was the first overdrive to use the JRC 4558D integrated circuit (IC) chip. It is the most important component to the Tube Screamer sound and is responsible for its thick, vocal-like, mid-range tone. 
The 808 was only in production for a couple of years before it was changed to the TS9 version in 1982. Because sales were poor in the beginning, that model was dropped by 1984. For a few years they changed the models and names frequently until the late 80s and early 90s when guitarists started to use them more frequently. By 1993, Ibanez settled on the TS9 due to its popular demand. The surge in demand had a lot to do with a guitar player from Texas.
Stevie Ray Vaughan, King of the Tube Screamer
Gear-nerd-folklore likes to claim that Vaughan was a big fan of the TS808. However, close examination of stage photos, recorded live video, insurance documents and customs declarations reveal that the TS9 was his preferred choice from 1982 through most of the 80s. Vaughan was said to have used his TS9 as a clean/solo boost that he would use to push the front end of his Fender Vibroverbs. He'd keep the level control on his Tube Screamer turned all the way up and the drive control set at a low gain stage.
In 1988, the Ibanez TS10 Tube Screamer replaced the original TS9 on his pedal board, which Vaughan generally used to generate higher gain distortion, with both the drive and level controls boosted, a sound that wasn’t otherwise available from his Dumble and Marshall Major amps. 
I would be willing to say with a great amount of certainty that Stevie Ray did more for the sheer sales volume of the Ibanez TS9 and TS808 than any other guitar player before or since.
He died tragically in 1990 at age 35, but at that point he was already a living legend, and it's no coincidence that the height of his creative powers coincide with the Tube Screamer's resurgance in the 80s.
SRV has one of the most sought after "tones" of any guitar player to ever live, and whether or not it really matters, the TS9 was an integral part of his live rig.
Tube Screamers, Are They Really That Good?
Well, not all Tube Screamers are great. There are a few models that are not usually coveted because they were made with cheap parts. The TS5 and TS7 "TONE LOK" models are a canonical example of this. I could go into a great amount of detail about both of these pedals and reasons why they are probably the least desirable of all TS models, but mainly they were cheaply made, so they sound cheap. 
But, because tone is "subjective," it would be ridiculous to dismiss these models completely, you never know who's going to pull great tone out of something that's considered "junk" and then EVERYONE will have to have that model. For example, the TS10 which was made from 1986 to 1993, was not a very desirable model, until John Mayer started using them exclusively. Prices on these units have gone up considerably. 
There are many colors in the Tube Screamer rainbow
You Either Love 'Em or You Hate 'Em
Most people either like what a Tube Screamer does, or they don't like them because of what they do. But it's usually not so much what they don't or can't do. You simply either like their signature sound or you don't. A lot of it depends on the player and what they bring to the instrument with their fingers. For some players it's a great complement.
How to Use That Signature Sound
Tube Screamers have this smooth, mid-rangy character that colors the sound of the guitar player using them. For some people it's a very desirable overdrive sound. It adds some thickness to the notes and overall character to the player. Turn the level up and it adds a volume boost that can push the front end of an amp. Use one alongside another overdrive to add "more" to an already overdriven signal.
There's also a drive control that can sweep from a very little amount of gain or grit to a fairly hefty amount of saturation and overdrive sag. Again, the point of the Tube Screamer circuit is that it produces an overdriven "amp like" sound. Several sources over the years have claimed that the Tube Screamer was originally designed for guitar players who were using solid state amps, because you can't push a solid state amp to overdrive the way a tube amp overdrives naturally.
Back in the late 70s, solid state amps did not have the kind of capabilities that they do now, so the Tube Screamer was designed to provide what those amps inherently lacked. That being said, Tube Screamers work equally-well hitting a clean tube amp, and sound especially good hitting an amp that's already experiencing real tube overdrive.
They have a tone control that allows the player to boost highs or mellow out the sound by adding low end. Turning the tone control up or down will not increase or decrease the inherent mid-range bump that is the overwhelming characteristic of this pedal. And for that very reason, you either tend to love them or hate them .
Some Words of Advice
Remember that not all Tube Screamers are created the same. If you tried one out and were not impressed, try finding a mid-to-late 90s Japanese (Maxon) TS9. Still not impressed? Check out an Analog Man 808 mod. Or, get your hands on a vintage piece and see what all the talk is about. You can purchase one new for a around $99 bucks. If you don't like it, use that as an opportunity to "mod" your own Tube Screamer and send us a postcard from down the rabbit hole of boutique Tube Screamer clones.
Contributed by Desmond Smith. Wishing you all the best my fellow gear nerds. Stay tuned for more from me, desmachine and be sure to follow me on Instagram and Twitter @desmachine.