\citet{Dessart_2011}: Synthetic line and continuum linear-polarization signatures of axisymmetric Type II supernova ejecta
Linear polarization complements spectroscopy (line shape evolution) in revealing asymmetry in SN explosion. General observational consensus is that II-P event starts with small polarization that rises with time as the photosphere recedes into the ejecta, revealing the more and more asymmetric inner region. Observations of Ib/c, which are explosions of stripped-envelope progenitor show high polarization from the beginning since the asymmetric inner region is already shown. 
(However, a recent paper by \citet{Nagao_2017} argues that the observed polarization can also arise from CSM dust scattering light echo. In this picture, the polarization rises with time because the polarized scattered light becomes more dominant as the unpolarized SN light fades. I think that this can also explain the Ib/c observation if Ib/c generally has denser and/or more asymmetric CSM than II-P.)
Paper describes the way they model polarization in SNe assuming electron scattering only. The key takeaway is that one needs to take into account the asymmetric and non-point like emission from SN (before scattering) and the real scattering phase function in order to back out correct polarization prediction. The method they use is good for axisymmetric distribution. 
Processes that affect polarization:
Simulation approach: stellar evolution to reach Fe core collapse, then symmetric, 1D SN explosion simulation (how realistic is this?). Then the grid is manually distorted to introduce axisymmetric source, this can be done either by radial or latitudinal stretching: \(d(r, \mu) = d_{\rm 1D}(r)(r/(1+A_2 \mu^2)\) or \(d(r, \mu) = d_{\rm 1D}(r)(1+A_1 \mu^2)\) respectively. (How realistic is this? Can we improve this by using something more akin to planetary atmosphere simulation?)   
\citet{Dessart2015}: Numerical simulations of superluminous supernovae of type IIn
Application of methods in \citet{Dessart2011} to compute polarization from the output of spherically symmetric radiative transfer model (they used CMFGEN; \citealt{Hillier2012}). They showed that a prolate morphology with  \(\rho_{eq}/\rho_{pole}\approx3\) can give the observed ~2% polarization in SN 2010jl. 
***\citet{Nagao_2017}: Circumstellar Light Echo as a Possible Origin of the Polarization of Type IIP Supernovae
Polarization seen in II-P SNe can come from light echo by circumstellar dust. The light echo is delayed by the light travel time from the SN to the dust location, and this time delay for CSM located at r ~ 1017
cm is t = r/c(1-cos \(\theta\)) > 40 days. So tuning r and  \(\theta\) can get the delayed time such that the SN fades by the time that the echo starts. The light echo itself can be strongly polarized because it's caused by scattering at large angle. (I think this is a fine tuning problem unless we can observationally show that only some SNe have this polarization evolution.)
The paper assumes some dust scattering parameters like albedo (0.5), peak linear polarization (0.5), and the asymmetry parameter g = 0.6 (0 is isotropic, 1 is forward scattering). They considered 3 geometries: blob, disk, and bi-polar (which turned out to be pretty similar to blob). 
Key parameter is the time delay of the echo: \(\frac{l_0}{c}\left(1-\cos\theta_{\text{obs}}\right)\). If this is > SN fading timescale, then you'll get large max polarization since the polarized echo light is stronger compared to the faded SN. They also found that the dust optical depth around 2-3 is optimal (\(\tau\) too large, multiple scattering, too small, not enough scattered flux).
The disk model can produce double peaked polarization and/or orthogonal shift in the angle of polarization as the echo flux transition from coming from the disk edge close to the observer ("component 1", horizontal polarization) to the sides ("component 2", vertical polarization).  
Comparison with observation shows that the blob and bipolar models fit SN 2004dj and 2006ov well, although it can be just from the choice of peak polarization that the disk model doesn't fit. 
Action items:

Important SN polarimetry groups

Observations

A substantial number of SNe of all types have spectropolarimetric observation, mostly, if not all, in the optical. The major instrument for this science is SPOL, Kast, and FORS2.
To read:

Review papers: 

\citet{Wang_2008}: Spectropolarimetry of Supernovae
This is a very observation oriented review covering specpol of both Ia and CCSNe. It has an exhaustive list of all SNe with polarimetric observations, both photometric and spectroscopic. For CC, it went through all the subtypes, and conclude that all CCSNe are significantly polarized. The common II-P events have small polarization during the plateau then experience a jump in polarization as the SN enters the nebular phase. The interpretation for this observation is that the asymmetric inner core region is revealed. The best observation of this is from SN 2004dj (Leonard+ 2006). This interpretation is corroborated by the fact that IIb and Ib/c are polarized early on since the core is already revealed, although observations for these are sparse.
Morphology of the polarimetric spectra on the qu plane can be helpful. Recall that the angle of polarization is 0.5 arctan(u/q), so if a SN is axisymmetric, its specpol will fall into a line in the qu plane (constant PA, thus constant u/q). Any scatter perpendicular to that is a sign of deviation from axisymmetry. Varying PA across a line can produce a loop in the qu plane. 
\citet{Mauerhan_2015}

IIn

\cite{Mauerhan_2014,Reilly_2017}: SN 2009ip
\citet{Reilly_2017} FORS2 Optical specpol for SN 2009ip during the 2012 outbursts. 
About SN 2009ip
Polarimetric observations by FORS2 on the VLT, 35, 42, 64, 68, 73, and 83 days after the 2012b outburst
Interpretation of polarimetry

II-P

\citet{Mauerhan_2017}: SN 2013ej
This is the strongest polarization ever measured around II-P/L, ~1% even at early time. Line polarization rises up to 3%. Since p is high since early time, the authors suspect that CSM dust scattering must play some part. 
Some key conclusions:
"We note that although the physical interpretations we have considered are plausible and guided by theoretical expectations, none offer a unique solution to the data on SN 2013ej."
Some issues: