Resonance phenomena induced by delays are presented. We propose and discuss three very simple models. Unlike typical resonance phenomena, they do not require oscillating external forces. Therefore, the delay-induced mechanism can be the simplest in generating resonance. The first model is described by a simple non-autonomous delay differential equation. Its most notable feature is that its exact solution can be written down as a sum of Gaussian dynamics. We believe this is the first instance that such solution is obtained for non-autonomous delay differential equation. This capability enables the analysis of its frequency resonance behaviors. The second model is given by a slightly extended non-autonomous delay differential equation, whose exact solution can also be derived using Lambert’s W function. This model exhibits amplitude resonance, the properties of which can be analytically understood. The third model is a delay stochastic dynamics that incorporates both noise and delay. With suitably tuned values of the noise strength and the delay, it also exhibits frequency resonant behavior. This model is described by a stochastic delay dynamical map, or by a special case of a random walk with delay (“Delayed Random Walk”). In the latter description, we can again analyze resonant phenomena. These examples illustrate yet another rich phenomenon brought about by the element of delay.