What happens to neurotransmitters after synaptic transmission and why does this need to happen?
They experience reuptake.
During synaptic transmission, the neurotransmitters interact woth ion chambers, slotting into the receptor sites. This changes the channel's shape and allows ions to travel through.
Once they have opened the channel (sort of like a key), they diffuse back across the synapse to the sending neuron. They cross the membrane again via a neurotransmitter transporter. This is known as reuptake.
Reuptake is important as it helps recycle neurotransmitters but it also controls how long signal (resulting from a neurotransmitter release) lasts. This is important, as some reactions don't need to be active for long periods of time (e.g. if you smell smoke and start panicking, you don't want to still be panicking even when you realise it's just some burnt toast).
Sometimes, the body can experience difficulties wuth reuptake and this can play a part in many common disorders like depression and schizophrenia.
For example, in depression there is often an imbalance of serotonin, norepinephrine and dopamine. If we focus on dopamine (a neurotransmitter that contributes to the sensation of pleasure or happiness) and consider that, in depression, there is often a low level of this, then it becomes apparent that it is very difficult for someone with depression to feel "happy".
However, this also means that we can find ways to treat depression by leveling out the levels. Some drugs may do this by blocking the reuptake of these "happy" neurotransmitters (often serotonin), therefore allowing them to send that "be happy" message again!
It is worth mentioning that some neurotransmitters do not get reabsorbed, and instead diffuse or are broken down by enzymes.
This is explained further in the video below, which is well worth watching if you have a spare ten minutes:
I have also written an answer relating to what synapses are, which can be found here . I hope this helps; let me know if I can do anything else:)