Alcohol has a number of long term effects. Of course there is addiction but that doesn’t happen to everyone, because we are not all made the same way. Some people are unlucky that they’re biology has left them vulnerable to the chemical effects of alcohol. Alcohol is a chemical that actually has a complicated effect on the brain, but like all other addictive drugs it increases the availability in the brain of a chemical messenger (a neurotransmitter) called Dopamine. Dopamine, (and its relatives Serotonin and Noradrenaline), is released by the brain to change our behaviour.
For example, dopamine is important for learning about rewards and memory. If we train rats that alcohol is available in a particular cage and not another, they will learn to navigate their way to the alcohol cage if given the choice (this is called conditioned place preference). However if we block Dopamine signalling in their brains (by using drugs) they can no longer learn that. Dopamine teaches the brain what actions to do to get a reward, and alcohol and other drugs hijack dopamine signalling to train the brain to keep seeking out alcohol (like a fake reward). Dopamine is also important for controlling movement (people often stagger after a few drinks and loose coordination).
In the long term, the Dopamine system of the brain takes quite a bashing from being repeatedly pushed to its limits by alcohol. In response, there are chemical changes in the brain but it cannot perform as it had before alcohol use. Some of the processes that depend on dopamine, mentioned above like memory and control of movement, become very difficult for people who have taken large amounts of alcohol in the long term. This is known as Korsakoff psychosis (named after the Russian Psychiatrists who described it back in the 19 century).
These effects depend on the age of the person, how much they drank amongst other things but I hope that gives you some idea, don’t hesitate if you’ve other questions!