The short answer:
World Space rotation order: XYZ
Local Space rotation order: ZYX
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The rotation order in terms of World Space is XYZ.
A simple test:
Select an actor in your scene. Make sure you’re in Rotation Mode (or press E).
Rotate around the X axis an arbitrary amount, like 50 degrees.
You’ll notice that as soon as you finishing rotating, the rotate tool will look exactly the same, with the Red, Green, and Blue rotate handles oriented the same way. This is because you’re rotating in World Space. If this were local space, the handles would rotate with the object.
Note the rotation value that shows up in the Detail panel is the same amount you rotated by.
Next rotate around the World’s Y axis by an arbitrary amount, like 20 degrees.
In the detail panel, the X rotation value will be the same, but now the Y value should reflect how much you just rotated by.
This is because the X rotation is independent of the Y rotation. If you rotated around the Y axis first and then the X axis, you’d notice that the Y rotation value would change. This is because the Y rotation is dependent on the X rotation.
Finally, rotate around the World’s Z axis by an arbitrary amount. Try rotating in any other order. You’ll notice values change unexpectedly.
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Conversely, if you want to rotate in local space, simply reverse the rotation order: ZYX.
A simple test:
Select an actor in your scene. Make sure you’re in Scale Mode (or press R). This is just to show you the actor’s local axes.
Using the Transform section of the actor’s detail panel, set the Z rotation to an arbitrary value, like 45.
You’ll notice your actor has rotated around its Z axis (the blue axis).
Now setting the Y rotation to an arbitrary value will rotate around the actor’s local Y axis. Notice the cube representing the actor’s Y axis hasn’t moved in space.
Finally, setting the actor’s X rotation will rotate it around its local X axis.
