3^4

Visit Notation to get an overview of the different notation systems to describe moves on the 3^4.

RKT

Summary

RKT is a general technique that is used to execute moves that damage fewer pieces. By using RKT, the solver picks a cell that the solver wants to treat i.e. as a 3^3 (If it was a 4^4 you were solving, RKT would treat a cell as a 4^3). The main idea is to only use RK and T- moves.
For example,

On a 3^3, you can do the sune algorithm: R U R' U R U2 R'. This is an OLL algorithm that can be used to orient corners, but is also able to permute edges (while breaking corners).
On a 3^4, if you replace the algorithm above like so: R=RU, U=TU, you can see that the algorithm seems to have moved 3x1x1x1 blocks. That means that 2c, 3c and 4c are all moved. What if you only want to affect the 3c and 4c of the top 3x3x1x1 block of the T cell? (aka the TU ridge)
Well, back on the 3^3, you can execute sune by doing only R turns and cube rotations. This becomes R z R z' R' z R z' R z R2 z' R'. Notice that the z turn brings the U face into the position of the R face, and the z' turn brings back the original R face.
Now to convert the 3^3 algorithm from the previous step into an RKT algorithm, just substitute R=RK and z=TF. Notice how the T cell seems to be affected in the exact same way the 3^3 was affected in the last step; treating the T cell as a 3^3, it seems to undergo z and R turns.

Note that even though this technique is called RKT, it is not limited to those types of turns. Thus, you can use LK and T- moves instead, or rotate your view and use RU and D- instead of RK and T-!

Cancelling

You can abuse symmetries of the puzzle to cancel your RKT to take up less moves. This is most applicable during the execution of algorithms. The gif below shows the difference in the Sune algorithm when executed purely with RKT and when using cancelling.

This is most easily understood in the form of the sexy move algorithm R U R' U'. When you click on the TRU sticker, the R and U layers that you were using for RKT swap with each other.