I would say one thing we realize is that we understand relatively little about how the brain functions. It was only within the last 10 years that we realized the majority of the energy consumption by the brain is not used for conscious response to the outside world (Dark energy ). We discovered the default mode network which is more active during rest and sleep than during attentive states.
energy consumed by this ever active messaging, known as the brain’s
default mode, is about 20 times that used by the brain when it responds
consciously to a pesky fly or another outside stimulus. 
Neuroscience can explain why so many people believe they have been abducted by aliens. There is a phenomenon called sleep paralysis which is surprisingly common. In
surveys from Canada, China, England, Japan and Nigeria, 20% to 60% of
individuals reported having experienced sleep paralysis at least once in
their lifetime.  Sleep paralysis can occur when you are falling
asleep or waking up. When you are falling asleep the body will go into
REM sleep while you are still aware. You can also become aware
before a REM cycle is complete. The significance of this is that while
in REM sleep you are in a state called REM atonia  which paralyzes
your body so that you do not act out your dreams. So when people
experience sleep paralysis they are conscious but not able to control
their body. Often times this can be accompanied by
"hallucinations/dreams" and people will attribute the bizarre experience
to an alien abduction.
Body image, the brain can believe that an amputated limb is still there. This is called the phantom limb and it is very common. Approximately
60 to 80% of individuals with an amputation experience phantom
sensations in their amputated limb, and the majority of the sensations are painful.
 This can be a very painful syndrome because the phantom limb will
often get stuck in a extremely painful cramped position and the amputee
will have no way to stretch the limb and stop the pain. The phantom
limb was essentially untreatable until one neuroscientist, Dr.
Ramachandran came up with a remarkably simple treatment. All he did was
make a box with a mirror in it and had the amputee put his intact limb
in one side and the amputated limb behind the mirror on the other. The
amputee then moved the intact limb and saw in the mirror his phantom
limb moving which tricked his brain into relieving the pain in the
phantom limb. Although the brain is incredibly advanced and
"intelligent" it is remarkably easy to trick it.
This was an answer I wrote on Quora.