Interstellar dust reveals its presence in astrophysical environments and its (both positive and negative) role in astrophysics mainly through its interaction with electromagnetic radiation (see Li  for a recent review):
obscuring distant stars by the absorption and scattering of starlight by dust (the combined effects of absorption and scattering are called extinction);
reddening starlight because the extinction is stronger for blue light than for red;
generating "reflection nebulae" by the scattering of starlight by dust in interstellar clouds near one or more bright stars;
generating the "diffuse Galactic light" seen in all directions in the sky by the diffuse scattering of starlight of stars located near the Galactic plane;
generating X-ray halos by the small-angle dust scattering of X-ray sources;
polarizing starlight as a result of preferential extinction of one linear polarization over another by aligned nonspherical dust;
heating the interstellar gas by ejecting photoelectrons created by the absorption of energetic photons;
and radiating away the absorbed short-wavelength radiation at longer wavelengths from near infrared (IR) to millimeter (mm) in the form of thermal emission, with a small fraction at far-red wavelengths as luminescence.
In order to correct for the effects of interstellar extinction and deredden the reddened starlight, it is essential to understand the absorption and scattering properties of interstellar grains at short wavelengths (particularly in the optical and ultraviolet [UV]). The knowledge of the optical and UV properties of interstellar dust is also essential for interstellar chemistry modeling since the attenuation of UV photons by dust in molecular clouds protects molecules from being photodissociated. The knowledge of the dust emission properties at longer wavelengths are important (i) for interpreting the IR and submillimeter (submm) observations of emission from dust and tracing the physical conditions of the emitting regions, (ii) for understanding the process of star formation for which the dust is not only a building block but also radiates away the gravitational energy of collapsing clouds (in the form of IR emission) and therefore making star formation possible, and (iii) for understanding the heating and cooling of the interstellar medium (ISM) for which interstellar dust is a dominant heating source by providing photoelectrons (in the diffuse ISM) and an important cooling agent in dense regions by radiating in the IR (see Li & Greenberg  for a review).
Ideally, if we know the size, shape, geometry and chemical composition (and therefore the dielectric function) of an interstellar grain, we can calculate its absorption and scattering cross sections as a function of wavelength. If we also know the intensity of the illuminating radiation field, we should be able to calculate the equilibrium temperature or temperature distribution of the grain from its absorption cross section and therefore predict its IR emission spectrum.
However, our current knowledge of the grain size, shape, geometry and chemical composition is very limited; the nature of interstellar dust itself is actually mainly derived from its interaction with radiation (see Li  for a review):
from the interstellar extinction curve which displays an almost linear rise with inverse wavelength (-1) from the near-IR to the near-UV and a steep rise into the far-UV one can conclude that interstellar grains must span a wide range of sizes, containing appreciable numbers of submicron-sized grains as well as nanometer-sized grains;
from the wavelength dependence of the interstellar polarization which peaks at ~ 0.55 µm, one can conclude that some fraction of the interstellar grains must be nonspherical and aligned by some process, with a characteristic size of ~ 0.1 µm;
from the scattering properties measured for interstellar dust which are characterized by a quite high albedo (~ 0.6) in the near-IR and optical and a quite high asymmetry factor (typically ~ 0.6-0.8 in the optical) one can infer that a considerable fraction of the dust must be dielectric and the predominantly forward-scattering grains are in the submicron size range;
from the IR emission spectrum of the diffuse ISM which is characterized by a modified black-body of -1.7 B(T = 19.5 K) peaking at < ~ 130 µm in the wavelength range of 80 µm 1000 µm, and a substantial amount of emission at 60 µm which far exceeds what would be expected from dust at T 20 K, one can conclude that in the diffuse ISM, (1) the bulk interstellar dust is in the submicron size range and heated to an equilibrium temperature around T ~ 20 K, responsible for the emission at 60 µm; and (2) there also exists an appreciable amount of ultrasmall grains in the size range of a few angstrom to a few nanometers which are stochastically heated by single UV photons to high temperatures (T > 50 K), responsible for the emission at 60 µm (see Li );
from the spectroscopic absorption features at 9.7, 18 µm and 3.4 µm and emission features at 3.3, 6.2, 7.7, 8.6 and 11.3 µm which are collectively known as the "UIR" (unidentified IR) bands, one can conclude that interstellar dust consists of appreciable amounts of amorphous silicates (of which the Si-O stretching mode and the O-Si-O bending mode are respectively responsible for the 9.7 and 18 µm features), aliphatic hydrocarbon dust (of which the C-H stretching mode is responsible for the 3.4 µm feature), and aromatic hydrocarbon molecules (of which the C-H and C-C stretching and bending vibrational modes are responsible for the 3.3, 6.2, 7.7, 8.6 and 11.3 µm "UIR" features), although the exact nature of the carriers of the 3.4 µm feature and the "UIR" features remain unknown.
The inferences from observations for interstellar dust summarized above are quite general and model-independent. But these inferences are not sufficient to quantitatively derive the absorption and emission properties of interstellar grains. For a quantitative investigation, one needs to make prior specific assumptions concerning the grain size, shape, geometry and chemical composition which are still not well constrained by the currently available observational data. To this end, one needs to adopt a specific grain model in which the physical characteristics of interstellar dust are fully specified. While a wide variety of grains models have been proposed to explain the interstellar extinction, scattering, polarization, IR emission and elemental depletion, so far no single model can satisfy all the observational constraints (see Li  and Dwek  for recent reviews).
In view of this, in this article I will first try to place constraints on the absorption and emission properties of interstellar dust based on general physical arguments; these constraints are essentially model-independent.
In astrophysical literature, the most frequently used quantities describing the dust absorption and emission properties are the mass absorption coefficient (also known as "opacity") abs with a unit of cm2 g-1, and the emissivity , defined as the energy emitted per unit wavelength per unit time per unit solid angle per unit mass, with a unit of erg s-1 sr-1 cm-1 g-1. The Kirchhoff's law relates to abs through = abs() B(T) if the dust is large enough to attain an equilibrium temperature T when exposed to the radiation field, or = abs() 0 dT B(T) dP / dT if the dust is so small that it is subject to single-photon heating and experiences "temperature spikes", where B is the Planck function, dP is the probability for the dust to have a temperature in [T, T + dT]. Other often used quantities are the absorption cross section Cabs and absorption efficiency Qabs, with the latter defined as the absorption cross section Cabs divided by the geometrical cross sectional area Cgeo of the grain projected onto a plane perpendicular to the incident electromagnetic radiation beam (Bohren & Huffman ). For spherical grains of radii a, Cgeo = a2 so that Qabs = Cabs / a2. By definition, abs = Cabs / m = Cabs / (V), where m, V and are respectively the dust mass, volume, and mass density; for spherical grains, abs = 3Qabs / (4a ).
In Section 2 I will apply the Kramers-Kronig relation to place a lower limit on (the wavelength dependence exponent index of abs) and an upper limit on the absolute value of abs. The state of our knowledge of interstellar grain opacity will be presented in Section 3 (with a focus on ) and in Section 4 (with a focus on the absolute value of abs), followed by a summary in Section 5.