I only worked with koans for a short time, and was pretty slow, but here are just a few things I noticed about them in general.
To put it roughly, koans work from the absolute and the relative sides, with Big Mind and our human self, and how Big Mind/Heart can be expressed through our human self.
Each koan has a different emphasis and focus, similar to a prism filtering light so we can explore the different aspects of it more closely. And each koan has a specific and unique resolution, which becomes obvious when it is seen, and something to work with in terms of bringing it into daily life.
Koans invite what we are to notice itself. After a while, thoughts tend to exhaust themselves, inviting in a release of identification from thoughts. And the resolution to the koan can often only be found from the Big Mind/Heart side, from shifting into and finding ourselves as Big Mind/Heart.
They invite in specific insights into what and who we are, through emphasizing specific aspects of Big Mind/Heart and how it can be expressed through our human self.
And they invite us to explore, through our daily life and in specific ways, how what we are can be expressed through who we are. (When I worked with koans, my daily life was often infused with the koan, there was no separation between working on it on the cushion or through daily life. And as it clarified, there was a curiosity about how to express it, live it, in daily life.)
This is one of the many things about Zen I appreciate. It is very much focused on what we are noticing itself. But it is no less focused on how it is lived through this human life, in a healthy, mature, thorough and skillful way.