Down regulation of the body's own neurotransmitters occurs (including dopamine) in many cases. Also, in the case of opiate abuse, the body's natural endorphins are not produced, sufficiently.
Problems which accrue include diminished sensitivity to pain, lower frustration tolerance and, ultimately addiction which can lead to an inordinate amount of time acquiring and using drugs as opposed to leading a more productive, satisfying lifestyle.
This is just a general overview, and the experiences of any given individual can vary greatly, especially depending on whether use is occasional versus daily and chronic, and depending on one's genetic susceptibility to addiction - or not.