The bottom line from the Large Hadron Collider, so far, has been that (1) a new boson that is a good fit so far for the Standard Model Higgs Boson has been discovered and (2) all of the data gathered so far, which probes up to the 1 TeV energy scale, confirms an unmodified Standard Model prediction.
In other words, up to the 1 TeV energy scale, the has been no discovery of new, beyond the Standard Model physics at the LHC.
Of course, as theorists are quick to remind us, it is always possible that beyond the Standard Model physics could appear at energy scales greater than those probed so far. Maybe there aren't any effects that can be reliably discerned until one reaches the 5 TeV energy scale, for example.
The Standard Model As A Low Energy Effective Theory
Even many strong proponents of the Standard Model who are deeply skeptical of the leading beyond the Standard Model theories circulating today will often acknowledge that they too believe that the Standard Model is more likely to be a low energy effective theory. The Standard Model may simply capture the "low energy" behavior of the true, deeper, ultimate laws of nature that applicable in all circumstances. In these context, "low energy" means the kind of situations that we can observe in our laboratories on Earth which are pretty feeble compared to the awesome scale in time, space and matter-energy involved to the universe itself.
The Particle Physics Desert
The Standard Model's resiliance at high energies owes quite a bit to the concept of "running constants." It has formulas that explain how the strength of the three forces it describes vary with the energy scale of the interaction. Those three forces are the electromagnetic force, the strong nuclear force that holds quarks together in protons and neutrons which also holds atomic nuclei together, and the weak nuclear force that brings about the decay of heavy atoms and exotic subatomic particles.
If you do the math, adjusting for special relativity, but not any general relativistic or quantum gravity effects (which is what the Standard Model does), these forces become almost identicial in strength at a point known as the Grand Unification Theory scale, which appears to be a "natural" place to look for new physics. The Grand Unification Theory (GUT) scale is at about 10^13 TeV.
A few orders of magnitude greater than that, and also a strong candidate for new physics is the Planck scale (10^16 TeV), derived from combining fundamental physical constants in a way that produces a set of man made arbitrary units (they are called "natural units" but I've overused that term in this post and want to be clear about the intended meaning). At energy scales greater than the Planck scale, the Heisenberg uncertainty principle starts to wreck havoc on the equations of quantum physics and many quantum gravity theorists have doubts about whether a description of space-time as a continuous manifold (as it is modeled in both the Standard Model and General Relativity) is an accurate description of the universe a such high Planck scale energies and at the tiny distances of the Planck legth.
A core open question in particle physics is whether there are any new physics in the "desert" between the 1 TeV scale phenomena that are experimentally bound and the GUT scale. Wikipedia explains the concept:
In particle physics, the desert refers to a theorized gap in energy scales between the TeV scale and the GUT scale in which no new physics appears. The idea of the desert was motivated by the observation of approximate, order of magnitude, gauge coupling unification at the GUT scale.
Is There An Oasis In The Desert?
Most active research in theoretical physics that is open to the possibility of beyond the Standard Model physics, proposes new physics that can be observed at the low end of the desert, a threshold that continually rises in energy scale as new experiments are conducted without finding new physics. Most supersymmetry theories (and most other GUT theories and many quantum gravity theories) predict that new physics (often subtle) will be discernable in the desert. For example,"[i]f neutrino masses are due to a seesaw mechanism, the seesaw scale should lie within the desert. . . . An alternative to a desert is a series of new physical theories unfolding with every few orders of magnitude increase in energy scale." Supersymmetry proponents hope to identify new supersymmetric particles, the lightest stable one of which could also explain dark matter phenomena seen by astronomers, typically visible at interaction scales of 1 TeV to 20 TeV or so, and having masses on the order of 100 GeV or more (i.e. close in mass to the Higg boson or heavier).
The less skeptical view holds open the possibility that new physics are "just around the corner" and will be discovered, if not during our own lifetimes, during those of our children or grandchildren or great-grandchildren if only our society is committed enough to finding it.
The conservative view is that there are probably no new physics in the desert, and that energy scales we have any serious hope of probing experimentally in the next few decades, or even centuries, are too tiny relative to the GUT scale to show any experimental indication of GUT scale physics. In other words, we are unlikely to discover beyond the Standard Model physics in any experiments that we can conduct in even the dimly foreseeable future.
How Huge Are GUT Scale and Planck Scale energies?
The interactions that are being probed at the Large Hadron Collider involve energy levels that have not been important in the cosmology of the universe after the first microsecond of its existence. We are fairly comfortable that, with the exception of dark matter, pretty much everything that has happened in the universe since then can be explained with the plain vanilla Standard Model of Particle Physics and plain vanilla General Relativity.
(So called "dark energy" isn't really a mystery as adding a single constant into the equations of General Relativity, as Einstein realized might be necessary a century ago, fully explains the observed effects of this phenomena. There are some loose ends in the area of neutrino physics that we haven't yet figured out, but we have good reason to believe that we may be able to figure out those issues within a few decades by simply filling in some only vaguely known values for Standard Model constants and figuring out at what rate (if any) neutrinoless double beta decay occurs.)
Put another way, pretty much all of the expansion of the universe after the first nanosecond (i.e. 10^-9 seconds) after the Big Bang has taken place at energy levels where the Standard Model and General Relativity are valid, and has expanded in size at the speed of light in the roughly 13.7 billion years since then. But, we aren't terribly sure precisely what dimensions the universe had during the first nanosecond of the universe, except that it was 13.7 billion light years across smaller than it is now. One estimate is that the universe was about one foot (10 cm) across at the end of the inflation period that started at around 10^-32 seconds after the Big Bang and might have been as much as seven feet across at the end of the first nanosecond.
(Purists will note that I'm cheating somewhat here, as General Relativity doesn't assign absolute times and distances to universe scale phenomena since these are observe dependent quantities even though there is a consistent way to reconcile the observations of all observers.)
It may require new physics beyond the Standard Model and General Relativity to explain the cosmology of the universe in this first nanosecond of its existence and this is what physicists are looking for now.
Reproducing the energies last routinely found in the universe in its first nanosecond, even if only fleetingly and in tiny volumes of space, is a challenge even for high eergy physicists that is to some extent a fundamental one, since the Big Bang cannot presumably, be reproduced (and we probably wouldn't want to do that even if we could). Squishing the universe (or even a tiny part of it with equivalent matter-energy density) into a package smaller than a compact car is unthinkable as an engineering proposition even with innovations over the entire lifetime of our species.
It isn't at all clear that physics involving interactions at scales where the Standard Model ceases to be an accurate effective low energy approximation of the true laws of the universe (or quantum gravity theories) would have any engineering applications, and even their cosmology implications would apply only to the first nanosecond of the universe's existence. The higher the energy scale beyond 1 TeV at which we fail to find new physics, the more true this conclusion becomes.