Neurons often exhibit considerable fluctuations in their spontaneous (stimulus-free) activity, characterized by correlation functions. Neurons also react to time-dependent stimuli described by response functions. Because the neural raison d'etre is information processing and transmission (shaped by both their fluctuation and response properties), one might wonder whether the two aspects (correlation and response functions) are related, and if so, how? In statistical physics such relations have been studied under the label of fluctuation-dissipation theorems. In neuroscience fluctuation-response relations (FRR) for spiking neurons have been discovered only recently. I review recent results on FRRs for general integrate-and-fire models that include spike-frequency adaptation, a refractory period, a colored Gaussian, or a Poissonian shot noise and discuss several applications of these relations.