The brain is made up of multiple neuronal connections.The nucleus accumbens is the part of the brain most associated with pleasant feelings like calmness, satiety, happiness and pleasure. Reinforcing connections in the nucleus accumbens can strengthen certain reward pathways, creating an addiction.
Drugs that are addictive often interfere with neurotransmitters, which are chemicals compounds produced by a neurone, and are responsible for transmitting the signal from one neurone to the next. Normally neurotransmitters remain in the synaptic cleft, the gap between two neurones, for only a short amount of time before they are taken up by the neurones and recycled. However, addiction-causing drugs will interfere with the re-uptake process, leading to continued activation of the reward pathway.
Over stimulation of the neuronal pathways in the nucleus accumbens is what leads to the initial feeling of euphoria after taking a drug. Taking the drug over long periods reinforces the reward pathways by overstimulating the neurones. After a while, the brain adapts, and becomes less and less sensitive to the reinforcer (drug). Higher doses of drug are then required to achieve the same euphoric effect, and an addiction cycle starts, that is often hard to break.
The reward pathway and addiction, NIH website, January 2014
Understand Addiction, Harvard Health Publications, January 2014
Neuroanatomy and Physiology of the “Brain Reward System” in Substance Abuse, Institute for Behavioural Genetics, January 2014