Near equilibrium, linear response theory has proven to be a powerful tool. At its core is the fluctuation-dissipation theorem, which dictates that the variance of small fluctuations is intimately related to dissipation. However, far from equilibrium no such equality exists. I will show that arbitrarily far from equilibrium dissipation still plays a dominant role in shaping fluctuations, both small and large, through some novel inequalities. In particular, I will discuss the thermodynamic uncertainty relation and its variants, which are universal nonequilibrium constraints between the variance of fluctuations and dissipation. These predictions offer general design principles for engineering artificial and natural nano-devices under energy restrictions.