The study of fluid-structure interaction involves many disciplines: from fluid dynamics, biological locomotion, mechanical engineering, geophysical phenomena to applied mathematics. In this talk, I will demonstrate a few examples when seemingly symmetric systems bifurcate into asymmetric and unstable states as a result of close interaction between structure and fluid. In particular, one example shows how a "symmetric bird" or a symmetric wing, once flapped up and down in a fluid environment, could "take off" and sustain a unidirectional flight. Another example shows that a model-continent, when interacting with a convective mantle, results in oscillatory or trapped states. Further, I will discuss a recent experiment that was inspired by the superrotation of the solid core of the Earth, as a symmetric structure takes a spontaneous spin in a symmetric cavity that contains fluid undergoing turbulent thermal convection. These phenomena were first found experimentally, and the results have been investigated by further experiments and numerical studies.