Invincible fighters and limbs interact with other objects and fighters—it isn’t like passing through a ghost, like intangibility—but the invincible fighter doesn’t flinch or take any damage. Unless aim is off, this means invincible moves usually win out, if contesting moves clash during invincible frames. Everyone is invincible while executing throw moves on opponents. Invincible attacks are rare, but include several shell-related Bowser moves, and the armored belly portion of King K. Rool’s move set, among others.
As with intangibility, invincible hurtboxes can be displayed in Training Mode. Invincible hurtboxes show up as green bubbles. (The easiest way to see this is to grab and throw the CPU dummy.) With the blue intangibility bubbles, green invincibility bubbles, and frame-skip feature, you can take as close a look as you like at move properties.