Neutral Monism—Overview
Neutral monism is the theory that all of reality consists of exactly one concrete object or thing, and everything that exists is, in some sense, that one concrete object or thing (or part of it). Because neutral monism seeks to account for both mental and physical aspects of reality—avoiding the metaphysical difficulties of dualism and overcoming the explanatory weakness of materialism and the decombination problem of idealism—it follows that neutral monism is also a major category of consciousness.

Several
Several Theorists
Several theorists offer their theories.
*This summary was verified by Robert Lawrence Kuhn.
Key Takeaways
Core Concepts
Reality is one unified entity; all mental and physical aspects are part of this single whole.
Scientific Context
Related to panpsychism but distinct; includes philosophical and metaphysical frameworks integrating mind and matter.
Why Meaningful
Offers parsimony, avoiding dualism’s split and materialism’s limits by uniting consciousness and reality in one substance.
Major Challenges
Boundaries with panpsychism blur; defining the “one thing” precisely remains philosophically and scientifically difficult.
Neutral Monism—Overview
Neutral monism is the theory that all of reality consists of exactly one concrete object or thing, and everything that exists is, in some sense, that one concrete object or thing (or part of it) (Schaffer, 2018). Because neutral monism seeks to account for both mental and physical aspects of reality—avoiding the metaphysical difficulties of dualism, and overcoming the explanatory weakness of materialism and the decombination problem of idealism (two other kinds of monisms)—it follows that neutral monism is also a major category of consciousness. In one way or another, neutral monism must cover or contain everything we call mental as well as everything we call physical. (The existence of various kinds of monisms does not much affect how monisms are theories of consciousness.)
There is substantial and obvious articulation, or overlap, between Neutral Monism and Panpsychism. Both are motivated by the need to integrate consciousness into the deep nature of reality; thus, monism theories have panpsychism features, and panpsychism theories can be seen as monisms (to first approximations). Perhaps it is simply the case of each reinforcing the other in what are merely different perspectives, historical and theoretical, on essentially the same stance regarding the fundamental nature of ultimate reality.
However, they are not entirely the same in that panpsychism has phenomenal or protophenomenal properties as a part or aspect of some larger, fundamental entity, while neutral monism has only one fundamental entity that encompasses everything (although it is not intuitively obvious that this distinction makes much of a difference). Separate categories for neutral monism and panpsychism are certainly justified, yet the boundary can be fuzzy.
In the psychosocial structure of consciousness studies, it would seem that almost everyone would like to be a Monist. Reality just seems more parsimonious with only one kind of thing, one stuff, rather than with two (i.e., Dualism), or, who knows, even with more. If the theory has a clear description of its monistic structure, its one thing, then it would be classified there (e.g., Idealism). The Neutral Monist theories here stress their monistic nature (which sounds like, but is not, a tautology).
Note that Spinoza and Leibniz together expose a strain in the Neutral Monism category. Leibniz's monadology is a pluralism—infinitely many simple substances—and its presence under Neutral Monism is defensible only on the loose reading that monads share one nature. With Spinoza directly above it, the contrast becomes conspicuous: to Spinoza, there is one substance, and, to Leibniz, there are infinitely many, both sitting together under a heading that says Neutral Monisms. Thus, the category covers unity-of-nature as well as unity-of-substance.
Moreover, some of the theories or ways of thinking that follow are categorized under Neutral Monism because all other categories seem less appropriate, imposing a belief system that should not apply. (I hope each of these theories feels less uncomfortable in Neutral Monism.)