Anxiety disorders are listed in the DSM4 & 5 however not all anxiety meets the criteria for a mental illness. Some anxiety can be a normal response to certain stimuli.
Anxiety is something we do, not something we 'have'. If someone for example has cancer, this can be observed irrelevant of whether they are awake or not, anxiety on the other hand is something only observable by our behaviours. The experience is very real, and can be debilitating, but anxiety is a process which requires us to do a set of things to experience the result. Because anxiety is something we do, it is something we can re-program our brains to stop doing! More on that in this program!