Frustrated systems, where interactions are such that they cannot all be
simultaneously satisfied, are amongst the most intriguing condensed matter
systems. In many cases, frustration is a direct consequence of the geometry of the underlying lattice - as in, for example, spins with antiferromagnetic interactions on a lattice of corner sharing triangles (Kagome) . This leaves the system delicately balanced between a variety of possible orders and even weak effects arising from quantum fluctuations or lattice displacements can cast the deciding vote. Complex orders can arise in this fashion - for example we discuss how frustration in a system of bosons leads to a supersolid state, where the system is at once both a crystal and a superfluid. Finally, we discuss how frustrated magnets are promising candidates for realizing spin liquid phases with exotic 'topological order', and recent experimental results that might be a first sighting of these unusual states.