What is so good about diffractive optics? What's so ingenious in diffractive lenses?
To my naive eye they seem to be just Fresnel lenses with smaller features.
What makes it so magic and why all the fuss about it?
 A: Here is a modern practical application of diffractive optics to solve a surgical problem.
When cataract surgery is done by an ophthalmologist (like myself), the cloudy lens of the eye is replaced by an artificial lens called an intra-ocular lens or an "implant" for short.
The standard implant, with its refractive optical design like a magnifying lens, creates chromatic aberration because its edges act as prisms. We know that prisms bend short wavelength light (e.g. blue) MORE than long wavelength light (e.g. red). Therefor a pinpoint light will be seen to have have a halo of chromatic aberration with a red outer edge.
A lens designed with diffractive optics also creates chromatic aberration, but in reverse: It bends short wavelength light LESS, etc. In this case a pinpoint light will be seen to have a halo of chromatic aberration with a blue outer edge.
Since chromatic aberration of either kind interferes with ideal sharp vision, the obvious solution is to use an implant designed with a combination of refractive and diffractive optics; the two kinds of chromatic aberration can be made to cancel each other.  
A: Diffractive optics aren't magic, they are simply another tool that can be used in designing an optical system. They can do things that refractive optics cannot, and they are often lighter and smaller than an equivalent refractive optic.
It is important to keep in mind, however, that the benefits of a Diffractive Optical Element (DOE) are not free. DOEs have limitations of their own. They are harder to produce, and typically produce the desired results only under very specific conditions.
For example, lets say you want to produce a circular laser beam with a very uniform intensity profile. What are your options for achieving this?


*

*Most laser sources produce a roughly Gaussian beam, so you could expand this beam heavily with a refractive expander, and then mask out everything but the center of the beam. This will give you a relatively uniform beam, but you will waste a lot of light.

*You could use a more complicated refractive design, like a micro-lens array. This is difficult to engineer, and won't give perfect results, but it can do a very good job under a variety of conditions. The beam intensity can be made uniform over a large distance, and the input beam to the micro-lens array will not need to be perfectly collimated. It will also work across a relatively broad wavelength range.

*Finally, you could design a DOE beam shaper. These can be designed to give any intensity profile you like, but it will be expensive to produce. It may (depending on what it is doing) have certain flaws characteristic of DOEs, like a strong zero-order beam (where a large fraction of input to the DOE passes through without being shaped). It may be very sensitive to errors in the input beam wavelength or collimation, and it may only produce the desired intensity profile over a short range of distances.
Like any tool available to a lens designer, DOE's have their uses. They can have very strong negative dispersion, which is often useful to correct chromatic aberration, and as I said they can be designed to produce arbitrary illumination patterns which would be outrageously difficult to make with purely refractive optics.
Lastly, while you can say they are "just Fresnel lens with smaller features," it is important to understand that a Fresnel lens is a diffractive optic, just a very simple one. In fact, when your understanding of diffraction is deep enough, you will realize that, in some sense, all lenses are diffractive optics. While you can engineer the phase profile of a DOE to produce a highly complex optical field, you could also design one to produce a simple focal spot; the resulting design would be a simple lens!
