Physicalist theories claim that everything is physical. Metaphysical physicalism has traditionally been called "materialism" or "materialistic monism": there's just one substance in reality, matter.
For eliminativism folk psychology and mental vocabulary refer to something which doesn't exist, they lack reference and are therefore useless to describe physical events of the "mental" kind.
Functionalism is a theory that takes psychological discourse to be a species of abstract, computational discourse. The theory was originally formulated as an alternative to the identity theory by Hilary Putnam who claimed that psychological descriptions are like Turing machine descriptions: abstract descriptions that postulate inputs, outputs, and internal states which correlate the two. Our brain would be mere hardware and our mind a software able to correlate inputs to a system with outputs from it in appropriate ways.
Anomalous monism which claims that everything is physical and that pyschological discourse is anomalous, that is, there are no laws that can be formulated using a psychological vocabulary.
Identity theory defends the ultimate reduction of mental states to brain states. For identity theorists mental states would be proven to be equivalent through the scientific investigation of the nervous system to physical states.
Behaviorism:it defended that psychology should concern itself only
with observable phenomena not even postulating inner causal mechanisms to explain overt behavior.