What are RPE and RIR?

In one line

RPE is a score you give yourself for how hard an exercise felt, and RIR is a count of how many more repetitions you had left when you stopped a set.

What are RPE and RIR?
The 'RPE 8' and '2 left' in workout plans
In strength training plans and gym talk you hear things like '3 sets at RPE 8' or 'stop with 2 left'. Both are ways to write down how hard you worked, not how heavy the weight was. This post explains what the two terms mean and how they connect.
In short
Two ways to put effort into numbers
RPE is a score you give yourself for how hard an exercise felt. RIR is the number of extra repetitions you still had in you when you stopped. Neither measures the weight. Both turn the effort you felt into a number.
First, reps and sets
One lift is 1 rep, a group is 1 set
Lifting a weight up and lowering it once is called a 'repetition' (rep). A group of reps done in a row without resting is called a 'set'. For example, if you lift 10 times and then rest, you have done 1 set of 10 reps.
RPE: the effort you felt
0 is sitting, 10 is all-out effort
RPE stands for 'rating of perceived exertion', a score for how hard something felt to you. It is often scored from 0 to 10, where 0 is sitting still and 10 is using every bit of effort you have. The same score is also used to describe how hard walking or running feels.
RIR: reps held back
How many more could you have done?
RIR stands for 'repetitions in reserve'. When you stop a set, it counts how many more reps you still had the strength to do. The moment you cannot do even one more rep is called 'failure'. If you stopped at failure, your RIR is 0.
The scale that links them
RPE 8 means '2 reps left'
Strength training has its own RPE scale that matches each score to the reps you had left. If you could not do one more rep, that is 10. If you had one more rep left, that is 9. The lower the score, the more reps you had left.
Why use this instead of weight?
The same weight feels different each day
Depending on sleep, food and stress, the same weight feels light one day and heavy the next. If you set an effort level such as 'RPE 8' instead of a fixed weight, you end up choosing a weight that fits how your body is that day. You lift heavier on good days and lighter on tired days.
How many to leave?
Close to failure, about 2-3 reps left
Strength training guidelines do not see a need to take every set to failure. Stopping close to failure, with about 2-3 reps left, also counts as enough effort. That is why workout plans sometimes say 'RIR 2-3'.
A common misconception
Is my guess of '2 left' accurate?
It is a little off. When people were asked to guess their remaining reps and then kept going until they truly could not, they did about one more rep on average than they guessed. Guesses were more accurate closer to failure and in heavier sets with fewer reps.
Summary
RPE is an effort score, RIR is reps left
RPE is a score you give yourself for how hard an exercise felt, and RIR is the number of reps you had left when you stopped. People tend to guess slightly fewer reps left than they really have. Related terms: 1-repetition maximum, training volume, progressive overload.