The most compelling and useful things I've read about communication in the past decade come down to one thing: the ability to recognise (in the moment or on reflection) what you and the other party are really talking about and adjusting accordingly.
The biggest problems in communication that might otherwise be cooperative and fruitful usually come down to some unrecognised mismatch between the parties.
Here are some of the forms in which I've encountered this:
Feedback
Thanks for the Feedback (Stone and Heen, 2014) lays out a model for why receiving feedback can feel so affecting. There is the matter of substance -- the truth of it -- the nature of the relationship between us and the feedback giver, and our tendency to extrapolate specific feedback to be an attack on our identity. In the case of 'identity' or 'relationship' triggers, we generally end up talking or thinking not about the specific feedback that's been levelled, but about a whole relationship or something fundamental to the stories we tell about ourselves.
They also split feedback into 'appreciation', 'coaching', and 'evaluation', which also has potential for expectation mismatch. If I show you a draft of a short story asking for 'feedback' -- by which I mean supportive appreciation about what you like so I'm not discouraged -- and you give me five pages of deeply detailed notes on what's wrong (evaluation), that's not going to feel entirely harmonious. Neither is more valid than the other, but the two parties being on different pages causes Problems.
Emotional Bids
A concept I remember hearing about on a podcast years ago, but for which I don't have the reference now. They studied couples and observed that one of the key factors for longevity and mutual communication was the response to 'emotional bids' -- one party saying or doing something which had some emotional stakes to them and which merited a response. Those stakes could be very small ('I saw this cool bird on my way back from work'), but it was them 'reaching out' to the other person in some form and looking for acknowledgement.
What they found was that recognising and responding to those emotional bids correlated with a longer relationship. Those responses need not be positive or the desired response, but the recognition that the other person was reaching out was critical.
Missing those cues and not understanding that there are emotional stakes in any given interaction is major communications problem.
Beliefs/Values/Morals/Ethics
I came across this first in Facing Violence, so I'll just quote from there:
People have a hierarchy of understanding and behavior—things that drive what they do, say, and are. At the lowest level of the hierarchy are beliefs. These are simply the things you hold to be true. These are not necessarily objective truths (diamond is harder than chalk) but often subjective truths: One can believe with absolute sincerity that the world is flat or round; that God does or does not exist; that people are basically good or basically selfish. Beliefs are our internal assumptions about the world and they lay the foundation for everything we do and say.
The next level up is values. Of all the things that we believe, some are more important than others. If you believe that God only allows prayer for healing and you believe that your child will die without an operation, which choice do you make? If you believe that politeness is critical to society but also believe that a certain individual only responds to anger, what do you do? You can see values in actions far more easily than in words. Beliefs and values, generally, are very deeply planted and not conscious at all. Morals derive from values and are your vague gut-level feelings about what is right and wrong. All of the things that you “just know are wrong” without being able to explain why constitute your morals. Ethics are your personal code, the general rules that you make up for yourself to try to put your morals into words. ... The ethics level is the most conscious, which lends to reasoned discourse, but it is also the least personal. An argument at the ethics level is not perceived as an attack on identity. An argument at the belief level, however, is very much an attack on identity. Arguing religion or politics, according to research, stimulates the emotional, not the logical parts of the brain. Telling someone one of their beliefs is wrong is telling them that they are stupid. It will be perceived as a personal attack.
...
You cannot successfully argue (or even really understand) from a higher level than the core disbelief. If someone disagrees with you at the belief level, you cannot convince him or her at any higher level. If you can explain yourself from a deeper level you are far more likely to get the other person to comprehend your point of view.
Facing Violence (Miller 2011)
Again, we see the same themes: stakes of emotion and identity that, when not understood by either party, lead to problems.
What's interesting to me is that I've encountered each of these at long remove from one another, over a decade or so. But they all echo the same theme, and, I realise now, are fundamental to my definition and understand of emotional intelligence. The ability to recognise these dynamics and to shift your thought and speech and action to address what we really talking about is paramount.