This is a rather complex area and I'm just barely beginning to scratch the surface of it, so I can't give much more than a cursory overview.
You are correct that they allow a build up neurotransmitter at the synapse,
this is relevant for all monoamine compounds, this includes most neurotransmitters and many hormones.
There are 3 main types of monoamine transport pathways as I understand it, one for serotonin and similar compounds, one for dopamine and similar compounds, and one for norepinephrine and similar compounds. Generally Monoamine oxidase is like a cleanup crew that comes in clears out any neurotransmitters hanging around in the synapse, of course inhibiting MAO inhibits this process allowing a build up to occur.
These compounds are also interesting in that they act on the benzodiazapine receptors. There are a plethora of beta-carboline compounds and each seems to have a little different effect and affinity at these receptors.
Some are agonists and have a similar effect to benzo's, some are inverse agonists and act basically as the opposite of a benzo, some are antagonists that block out the receptor such that other molecules cannot access it.
Then you have some that have SSRI effects.
Several of these compounds also function as anti-oxidants, and
have antimutagenic and antigenotoxic properties.
They function as neuromodulators.
They appear to play a role in learning and memory.
They have neuroprotective properties.
They play a role in endocrine and pituatary functioning.
They have anti-convulsive and anti-depressant properties.
These compounds are also used by plants to communicate with insects.
These are only a handful of the most basic effects, the easy part as it were. From here things get complex and I can't really explain very well because the jargon gets over my head. For example
tetrahydro-beta-carbolines are inhibitors of the mitotic kinesin KSP, which basically means they have anti-cancer effects.
Bromal-derived tetrahydro-beta-carbolines impair dopamine metabolism and mitochondrial respiration, which basically means they act as neurotoxins.
As stated before, this is only a very cursory overview barely scratching at the surface of the activity of these remarkable compounds. These compounds play a role in many biological processes and likely have dozens, scores even, of other effects. Hopefully this gives a least a little bit of perspective on the many functions of these important compounds.