I identify more as ethically nonmonogamous than polyamorous, and am a big fan of the notion of relationship anarchy. This means I do not have, nor do I want to have a "primary" partner in terms of a hierarchical relationship structure. This also means the delineation between relationships is far more fuzzy for me, and labels for said relationships is usually kind of pointless. I have people I consider to just be friends with whom there is sexual contact, and there are people with whom I have strong emotional bonds, but no sexual or romantic attraction. This is not to say that I don't have deep, intense, committed bonds, it's just that that said bonds don't have specific goals or intentions outside of honesty and enjoyment of shared company.
A large part of my attraction to this path is the lack of pre-scripted expectations for relationships. There are no labels that have deep cultural ties and expected behaviors, so each relationship follows it's own course. This is done mostly by attempting to be completely open and honest about one's feelings, both with one's partners and with one's self. Knowing and exploring your boundaries and limitations is a big part of being poly or non-monogamous for me. And being able to express these boundaries with the people in your life is a skill that can take time to learn, I'm still working on it myself and have been actively identifying this way for about seven years.
As for how my relationships function, I am seeing multiple people at the moment, though none are that serious. All are aware of each other, and some know each other outside of my connection with them. There are no established rules or expectations outside of honesty and openness, and even things like how much time is spent with each one in a given week/month is often very fluid. I religiously use Google calendar to keep up with my schedule, as dating/poly is one of many things that take up my time.
It can be complicated at times, but it feels far more natural to me than monogamy ever did. And I recommend that if one tries it, that they focus on honesty and communication above all else.