When electromagnetic radiation (photons) meet matter, it produces different effects on molecules, atoms or even nuclei. The higher the photon energy (frequency), the more volatile the effect.
In turn, most of these effects produce EM radiation when releasing that energy.

The possible interactions are

Transmittance	No interaction (let through)
Attenuation	Loses energy due to absorption or scattering
Absorption	Transforms into higher energy states of the matter
Scattering	Re-emitted in different directions after possible part absorption
Reflection^*	Bounce back at surface in one direction
Refraction^*	Bends at surface in one direction
Diffraction	Bends around objects with a discrete wave pattern
* Special cases (of scattering), but usually mentioned seperatly

Absorption (pure)

Non-ionising
	Nuclear magnetic resonance (NMR)	Nuclei in a magnetic field absorb and re-emit electromagnetic radiation of their resonance frequency
	Electron spin resonance (ESR)	Same as above but but for electrons
	Molecular rotation transition	Rotation of molecules (other than metallic conductors) Continuous spectrum curves with peaks
	Molecular vibration transition	Different kinds of vibration inside molecules change energy level
	Atomic electronic transition	Outer electrons change orbitals
	Molecular electronic transition	Outer electrons change orbitals Discrete spectrum lines
	Core electronic transition	Inner electrons change orbitals
Ionizing
	Ionisation	Liberating bound electrons from matter. Energy required depends on chemical make-up
	Photoelectric Effect	Liberating free electrons from the conduction band
	Nuclear events (γ rays)
	Pair production	particle and anti-particle are created

Scattering

Type	Elastic?	Description
Non-ionising
Brillouin	N	Atomic chain oscillations (typically solids). Waves are released or absorbed by photon and re-emit it with resp. a bit less or more energy caused by internal sound waves in the material
Mie	Y	Molecules larger than the incoming photons' wavelength. Re-emits not equally in all directions. Effect almost not wavelength dependent
Rayleigh	Y	Small molecules, (particles too). Absorb as vibrations(?) and re-emit it equally in all directions. Effect very wavelength dependent
Resonant	Y	Special case of Rayleigh or Raman, excites atom from initial to intermediate state
Fluorescent	N	Special case of resonant scattering
Raman	N	absorb, mostly as molecule rotovibrations, and re-emit radiation with less or more energy
Electronic Raman	N	absorb, as electron exciting, and re-emit radiation with less or more energy
X-ray Rayleigh	Y	absorb, mostly as ??as electron exciting??, and re-emit with same energy
Ionizing
Thomson	Y	oscillate and re-emit radiation in all directions, partly polarized----note to place on spectrum it should end where compton starts
Compton	N	absorbs as freeing of electrons, and re-emits with lower energy (inelastic form of Thomson scattering)
Elastic scattering re-emits the radiation with the same energy and thus same frequency as the incoming radiation. And any absorption interactions are temprary. So for the non-elastic scattering, some of the rest energy is absorped for a longer time.
The spectrum boundaries of some of the interactions are not precise, may be even plainly wrong. There was no time to find that information on the internet nor any physicist contact to ask for help. Check in the menu "? > About" to contact me to help me with this.

Fun facts

Surfaces described as white owe their appearance to multiple scattering of light by internal or surface inhomogeneities in the object
Selective absorption of certain colors, determines the color of most objects with some modification by elastic scattering. The apparent blue color of veins in skin is a common example where both spectral absorption and scattering play important and complex roles in the coloration.
Light scattering can also create color without absorption, often shades of blue, as with the blue sky (Rayleigh scattering) and consequently yellow sun, the human blue iris, and the feathers of some birds

More on molecular vibration and rotation

When matter contains heat, its molecules behave chaotically in many ways, moving relative to and bumping into each other, themselves thus rotating and vibrating.
Their own vibrations as well as the vibrations of their individual atoms relative to each other, have only a limited number of ways of doing that and only with discrete frequencies. Both depend on their configuration and bonds. In other words, depending on the chemical structure, the sorts of behaviors (vibrations) as well as the number of energy levels are determined. The more atoms a molecule has, the more simultaneouss vibrations as well as sorts of vibrations can be going on. But even a simple molecule can have a lot of different energy levels!
Some sorts of vibrations: stretching, bending, rotating, twisting, rocking, scissoring and wagging . And each has different subdivisions.

Now, we can imagine molecules by their orbitals. The vibration of these electron clouds from their normal state, creates moving uneven electric fields.

Each specific transition between two specific vibrations have very specific energy differences, which corresponds to discrete frequencies. When a molecule "cools down", it goes back to a lower vibration state and gives up that discrete energy in the form of EM radiation with the same frequencies (or heat).

And vice versa, any object can also absorb heat when the specific frequencies of the radiation fits with the possible vibrations within the object.

There is a useful theoretical body that can absorb all frequencies. Our sun behaves much like it. See "black body" for more.

P.S. Some texts make a clear distinction between vibrating and rotating. Here, we didn't and don't.

Interaction with matter

Absorption (pure)

Scattering

Fun facts

More on molecular vibration and rotation