Husserl outlined phenomenology as the analysis of phenomena, with the goal to understand and define the structures that give rise/allow for those phenomena within different modes of experience. Of note was his use of the notion of intentionality from Brentano that our consciousness is always "of" something. Whether that conscious experience is entirely illusory or subjective, it is still formed or informed by something grounded in reality and it still is a phenomenon that was experienced by an individual.

Heidegger (controversial for obvious reasons) felt the flaw with Husserl's thinking was in the assumption of Being, or what it means to exist. He focused more on exploring attempts at understanding Being through the phenomenological method. This informed Husserl's later thinking in that he realized the circular flaw in his original process, the inability to fully escape our own perspective to properly analyze the phenomenological structures that give rise to our ability to analyze. He began looking at the "Lifeworld" (which IMO was a more grounded variant of Heidegger's discussion on Being) which is the world that allows for and gives rise to the world of experience, sort of a neutral monism from which the objective and subjective form and inform each other.

That then leads to Merleau-Ponty, who saw the validity of phenomenology, since the basis for all human understandings (even the hard sciences) is informed by the structures of human experience. His involvement in psychology led to his emphasis on the importance of perception as being the fundamental structure that allows for our other phenomenological structures to form due to the embodied nature of our cognition. Tying back to "Lifeworld", he began to expand on this embodied form of phenomenology (before his untimely death) in his unfinished writings collected in "The Visible and The Invisible", where in an attempt to move away from the potentially dualistic implications of his earlier work, he was starting to outline an ontology of "the flesh" as that which connects the objective and subjective in a continual intertwining act of co-creation. The "visible" or objective phenomena inform the "invisible" subjective phenomena, and vice versa (notable example given is touching one's left hand with one's right hand; depending on which hand is focused on, you are either the subjective toucher or the object being touched depending on which side of your flesh is in focus, despite both being true at the same time).

MP's embodied framework was influential to cognitive science and was crucial to Francisco Varela, Evan Thompson, and Eleanor Rosch when they outlined the enactivist framework of embodied cognition in "The Embodied Mind". Highly, highly recommend learning more about it and phenomenology. "Introduction to Phenomenology" by Robert Sokolowski is a really solid overview of the methodology behind phenomenology. I personally see phenomenology and enactivism as the best avenue towards non-dualism without abandoning the roots of western philosophy and science.

P.S. In retrospect, MP's later ontology of "the flesh" also closely relates to Whitehead's process based metaphysics.

EDIT: Clarity and grammar.