What are the applications of cointegration?

We have had several posts on cointegration, and I must admit that I have only seen them mentioned here and there but I have no real experience using this concept.

My question is pretty simple: how do you use cointegration to create strategies?

In other words, in what fields are you using this concept?

Be careful: even if you have two processes $A_t$ and $B_t$ that you find to be cointegrated (ie as explained upper you have a linear combination of $A$ and $B$ that is iid), it does not mean that you can trade it.
It means that if you identified two parameters $\theta_A$ and $\theta_B$ such that $$C_t:=\theta_A A_t + \theta_B B_t \sim {\cal N}(0,v)$$
you can buy the residuals ($\epsilon_t = \theta_A A_t + \theta_B B_t - C_t$) of the regression against $C_t$ when they are cheap and sell them high, but only if you can trade it.
For instance, if $A$ is a stock or a future and $B$ is a macroeconomic indicator, you will not be able to buy and sell $B$. Some people nevertheless try to trade the cointegration just using $A$, because $C_t$ is cheap means cheap with respect to current economic conditions and because the macro variables are changing slower than stock prices, but they are exposed to macro trends or jumps.