i will provide an answer to this question along with answers to some of my comments on this thread (plus provide a couple of quick references).
Electromagnetic (EM) Radiation / Light interaction with matter (material objects) involves various things. Concerning opaqueness/transparency of materials the following figure shows what happens (reference: http://www.uotechnology.edu.iq/appsciences/filesPDF/material/lectures/2c/3-Materials_prperties8.pdf):
EM waves interact with a material through its (micro-)structure, meaning mostly electron/energy zones (plus nuclear structure, size of material, thickness, angle of incidence etc..)
The (detailed) effects are calculated using quantum-mechanics. Due to interaction of an EM wave with the structure of the material, the amount of reflection/absorption/transmission depends on the wavelength/frequency of the incident EM wave (related to Einstein-Planck relation $E=hv$, $E$ energy of EM wave, $h$ Planck's constant, $v$ frequency of EM wave)
In summary the micro-interaction is as folows:
a photon with given energy can interact with an electron (with a given energy) and make the electron jump to another orbit/energy zone, thus the photon is absorbed, or may be scattered/deflected by an electron, thus the photon is reflected/attenuated or might not interact (depending on photon energy/wavelength and energy zones of material), thus the photon is transmitted.
To characterise the amount of opacity/transparency of a material object (with respect to EM radiation of given wavelength), there are various coefficients used, based on Beer-Lambert Law (and similar formulas). For more detailed approximations one can check for example https://newton.ex.ac.uk/research/emag/pubs/pdf/Hooper_OE_2008.pdf
The (perceived) color of a material object, depends on what (visible) wavelengths reflects and absorbs. So a material which absorbs all (visible) wavelengths while reflects none would appear as "black", while a material which reflects all (visible) wavelengths while absorbs none would appear as "white". A material which reflects (visible) wavelengths around the "red" wavelength, would appear as "red", while a material which absorbs only wavelengths around (visible) "red" and reflects everything else would appear as the "complementary color of red" and so on.
It is clear form the above, that opacity/transparency of a material object is primary a function of light/EM wave frequency (or wavelength) (in general different for each material object). As such there are certain (ranges of) wavelengths of EM radiation with respect to which material objects are (mostly) transparent or (mostly) opaque.
Concerning metals (as per one comment), metals are mostly opaque in the range of visible light, while mostly transparent in the range of X-rays/$\gamma$-rays (reference: http://higheredbcs.wiley.com/legacy/college/callister/0470125373/conceptcheck_ans/ch19.pdf based on http://phys.thu.edu.tw/~hlhsiao/mse-web_ch21.pdf)
A physics.se question about transparency of plactic bags in infrared radiation
Anyone interested to experiment, here is a nice handbook on light measurement