What we know about the brain can be divided into 3 or 4 categories...

1: neurochemistry/neurotransmitters… it was discovered a hundred years ago that communication between nerves at their synapses is a chemical event involving neurotransmitters (chemicals) and receptors in the cell walls for these neurotransmitters.
Over the decades more and more details have been unraveled by numerous researchers. There are a handful of major transmitters (e.g acetylcholine, dopamine, GABA), and dozens of minor ones.

2. gross anatomy and connectivity. The gross anatomy has been studied over an even longer period, with ever more sophisticated tools. We used to do "ablations" studies: when you kill a nerve body its axons die off and you can trace their connections. Or a stain (and poison) horseradish peroxidase will spread down the axons.
Now we have functional MRI (fMRI) (and PET scans and other techniques) to see what areas are active and when.

3. behavioral studies: I said 3 or 4 because I'm not for how much we've learned from this aspect of study. The big names are Pavlov, Lorenz and Tinbergen (ethology). We have not learned that much of any importance (I think) from Skinner and the "Behaviourists", but there are many other observers, some crossing disciplines - like Sherrington's work on reflexes at the beginning of the 20th century… the study of connectivity, nerve nets!