As a representation of rotations, they have several flaws:

- a single rotation can be represented by several different sets of Euler angles, allowing a phenomenon known as gimbal lock
- it is difficult to compute the combination of sets of rotations within the Euler angle framework
- they are difficult to interpolate smoothly, or in a coordinate-independent way

The Euler angles form a chart on SO(3), the mathematical group of rotations in 3D space. See Charts on SO(3) for a fuller treatment.

Some naming systems for Euler angles include:

- "NASA standard aerospace" convention: "precession, nutation and spin";
- "heading, attitude and bank"

- G. J. Minkler, Aerospace Coordinate Systems and Transformations. Magellan Book Company, Balitmore, MD, 1990.