Benzodiazepines and their Euphoric effect how and why?

Benzodiazepines are a class of drugs that serve as positive allosteric modulators of the GABAA receptor by binding to their own "site" on the aforementioned receptor. By doing this they produce euphoria and a wide range of effects characteristic of Central Nervous System (CNS) depression (e.g. anxiolysis, sedation, amnesia, mental confusion, muscle relaxant effects).

benzodiazepines since they increase GABA activity, presumably also in the mesolimbic dopamine pathway thus producing dysphoria 

Benzodiazepines

But how do they do it??

Benzodiazepines do not bind to GABAA receptors universally. Thus the presumption that it inhibits the mesolimbic dopamine pathway may be wrong. They may not interact directly with said pathway at all.

Many subtypes for the GABAA receptor exist. The receptor consists of 5 subunits. The following subunits are known to exist: α1-6, β1-3 and γ1-3. The most common combination has two α, two β and one γ. You find ones with distinct compositions at distinct locations in the brain. All have two bindingsites for GABA, but only a subset has an additional binding site for benzodiazepines.

The benzodiazepine binding site is at the interface of an α and a γ subunit, so receptors without this structure will show no affinity for benzodiazepines. Additionally the α subunit must contain a histidine residue, which is only true for α1, α2, α3 and α5. That is paraphrased from wikipedia, where you can find the sources as well.benzodiazepines may not interact directly with the dopaminergic reward pathway, like opiates and cocaine does.Euphoria to be an indirect effect, resulting from the muscle relaxation (which will feel like you had a good massage), and the calmness of the mind.