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It is common to assert that the discovery of quantum theory overthrew our classical conception of nature. But what, precisely, was overthrown? Providing a rigorous answer to this question is of practical concern, as it helps to identify quantum technologies that outperform their classical counterparts, and of significance for modern physics, where progress may be slowed by poor physical intuitions and where the ability to apply quantum theory in a new realm or to move beyond quantum theory necessitates a deep understanding of the principles upon which it is based. In this talk, I demonstrate that a large part of quantum theory can be obtained from a single innovation relative to classical theories, namely, that there is a fundamental restriction on the sorts of statistical distributions over classical states that can be prepared. This restriction implies a fundamental limit on the amount of knowledge that any observer can have about the classical state. I will also discuss the quantum phenomena that are not captured by this principle, and I will end with a few speculations on what conceptual innovations might underlie the latter set and what might be the origin of the statistical restriction.

We prove that all non-conspiratorial/retro-causal hidden variable theories has to be measurement ordering contextual, i.e. there exists *commuting* operator pair (A,B) and a hidden state \\\\lambda such that the outcome of A depends on whether we measure B before or after. Interestingly this rules out a recent proposal for a psi-epistemic due to Barrett, Hardy, and Spekkens. We also show that the model was in fact partly discovered already by vanFraassen 1973; the only thing missing was giving a probability distribution on the space of ontic states (the hidden variables).

Cosmological observations will soon distinguish between the standard slow roll inflationary paradigm and some of its recently developed alternatives. Driven by developments in string theory, many new models include features such as non-minimal kinetic terms, leading to large non-gaussianities, making them observationally testable in the CMB. Models of slow roll inflation can also give rise to large non- gaussianities if the initial inflationary state was sufficiently excited, with a shape dependence that will be clearly distinguishable. I will review these different possibilities and discuss how they provide new theoretical challenges in understanding the initial conditions problem and the global structure of the inflationary universe.

The history of human knowledge is often highlighted by our efforts to explore beyond our apparent horizon. In this talk, I will describe how this challenge has now evolved into our quest to understand the physics at/beyond the cosmological horizon, some twenty orders of magnitude above Columbus\' original goal. I then recount how the study of physics on the horizon scale has led to the successful development of inflationary cosmology, and how we can use the Integrated Sachs-Wolfe effect in the Cosmic Microwave Background to probe cosmological physics, such as late-time inflation, the nature of gravity, and primordial non-gaussianity on the horizon scale.