I have known Nathaniel Craig since he was a brilliant Harvard undergraduate who was attending graduate courses – at least my string theory course (I believe he was the best student in the room). This young Gentleman has written 37 papers or preprints (if you subtract some namesakes) and the last one among them is sufficiently pedagogic for you to be interested in it:
The first section is an introduction. At the end of it, on page 5, Nathaniel summarizes 5 positive reasons why the LHC has strengthened our belief that SUSY is right and relevant and 1 way in which it has weakened the belief.
In the following section, he discusses the expectations – naturalness and parsimony (essentially minimality) of the right supersymmetric models. The section is summarized by an expected ordering of the superpartners' masses and reasons for this ordering.
The third section is about our knowledge, especially various limits. In this section, you start to encounter lots of handwritten yet colorful cartoons that reproduce various graphs that you might think that only computers can draw well. ;-) Colorful, electroweak, third-generation, Higgs-related superpartners are given special attention.
The fourth section is about indirect limits, mainly ones from various rare decays.
Implications of the Higgs and its suddenly known (SUSY-compatible) mass as well as Standard-Model-like couplings are discussed in Section 5.
There have been no signals proving SUSY reported by the LHC yet. This disfavors the minimal naive models and Nature reconciles SUSY with the observations in at least one of the two ways: by breaking the signal relatively to the most visible naive models or by breaking the spectrum.
Section 6 is dedicated to breaking of the signal. It's harder to see SUSY if the spectrum is compressed or SUSY is stealth or SUSY is R-parity-violating. Compressed spectrum means that the LSP isn't much lighter than the colored superpartners. If that's so, not many particles may be produced when the colored superpartners decay to the LSP and something else. Moreover, the missing transverse energy tends to cancel as it's copied from the oppositely moving colored superpartners.
Stealth supersymmetry has a light LSP (usually outside the MSSM) which decays into something truly "almost invisible", like a light gravitino, and its R-even superpartner whose mass is just a bit lighter than the LSP mass. This R-even superpartner consequently decays into well-known SM particles so almost nothing new – and, more importantly, almost no missing energy – is produced in the reaction.
R-parity violation makes it harder to economically explain dark matter and may worsen problems with the proton decay. For the latter reason, RPV operators should still preserve either lepton or baryon number. SUSY becomes less visible because the (new) superpartners may completely decay up to SM particles again.
Section 7 is about breaking of the spectrum. Natural SUSY became a newly recycled term for SUSY models where only particles that are "really needed" for the lightness of Higgs' being are light – especially the third-generation quarks (primarily the stops). Light stops have been discussed on TRF many times, of course. This lightness of the third generation should ideally be connected with the heaviness of the third generation of SM fermions. Such models are OK with the LHC data because the data still allow light third-generation sleptons and squarks; and there's nothing unnatural about the heavy (and safely LHC-compatible) first two generations of sfermions. Nathaniel discusses various strategies to obtain natural SUSY models by choices in the mediation.
By supersoft SUSY, he means a different way of breaking the spectrum. The squarks of all generations are comparably light but the gluino is much heavier which is enough to suppress the production of superpartners at the LHC (which is mostly performing gluon-gluon collisions, using a microscopic perspective). This would be unnatural in the minimal models but it's OK if the gluino is a Dirac particle, something that I like so it's been repeatedly discussed on this blog.
Nathaniel discusses one more unusual way of breaking the spectrum, folded or colorless SUSY, in which the relevant superpartners don't carry any color, unlike their known SM partners. I don't understand how this could be possible and will study this tonight. (I see, they're just some non-SUSY models that also cancel quadratic divergences but in a more general way. This looks contrived to me and the only way way how string theory could endorse such things is via some non-supersymmetric orbifolds.)
Focus point SUSY – another way to break the spectrum, a way that is considered rubbish by Nima Arkani-Hamed, by the way – is also dedicated a special subsection.
The final subsection of Section 7 is about minisplit SUSY – going in the direction of split SUSY by Arkani-Hamed et al. but not that extreme. In this approach, one sacrifices naturalness but tries to respect all the other attractive conditions.
The final Section 8 is dedicated to thoughts about the future and Nathaniel's recommendations how people should approach the 2015- LHC run at 13 or 14 TeV. Acknowledgements and 93 references are the only other thing expecting you after that section.