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Bosons with spin: An exciting new playground for exploring quantum many body physics

Ultra-cold bosonic atoms with large spin such as Chromium, Dysprosium and Erbium are a novel platform for studying quantum many-body phenomena, that has no analog in condensed matter. Experimentalists have not only successfully produced Bose condensates of these atoms but have now loaded them into optical lattices with non-trivial underlying band structures. What is the interplay between the large spin, single particle physics and interactions in these systems? In this talk, I will give an overview of the phenomenology of the simplest spinfull Bose gas, namely a spin-1 Bose gas. I will discuss the zero temperature physics in the continuum and in a lattice, and highlight the competition between various symmetry breaking orders at temperatures near the Bose condensation transition. Finally, motivated by very recent experiments at NIST, I will discuss the interplay between magnetism, liquid crystallinity and density wave order in a spin-orbit coupled, spin-1 Bose gas.