Drug Abuse can not be reviewed without linking it to Addiction.  Addiction can be physical or psychological and is sometimes synonymous with Dependence.  To keep it simple, Addiction means you really, really "WANT" something whereas Dependence means you "NEED" something.  

Sometimes, "need" is real such as when someone needs antibiotics to control a bacterial infection or when someone needs insulin to help control type 1 Diabetes.   Thus, it can be temporary or long term.  When the "need" is perceived or self-induced, such as when someone "needs" a cup of coffee in the morning to help wake up, it could lead to your body actually developing a real dependence which then makes your body "need" the cup of coffee.   

With physical Addiction, there is no "need", there is only want.  Your body rarely needs any of the substances you get addicted to but once it has them, it really wants them and it goes into something called withdrawal when they don't get it.  

Withdrawal can be very painful and makes a user have many symptoms that make them feel sick, agitated and place their nervous system into shock. This often leads people to doing irrational things that hurt themselves and others in order to obtain the drugs they want.  

The videos below explore and explain what happens in the brain.  In short, drugs (and some other things) literally cause a chemical (and sometimes structural) change in the brain because it "wants" more of the substance.    Some of the most addictive drugs are Nicotine, Heroin and Crack Cocaine.   

With psychological addiction, a user doesn't experience many, if any, withdrawal symptoms if they decide to stop using the substance.  A psychological addiction does effect the brain's pleasure centers and dopamine levels however, if a user stops, their body does not typically go into shock.  Because of this, many people say that drugs such as Marijuana, are not addictive.  In truth, the better term would probably be obsession as the effects and "withdrawal" symptoms are similar, for example, as someone obsessed with their cell phone.  The below videos speak mostly about physical addiction but do also mention some things that would be psychological addiction or obsession.