We propose a new type of optical resonator that consists of embedded ring resonators (ERRs). The resonators exhibit unique amplitude and phase characteristics and allow designing compact filters, modulators, and delay elements. A basic configuration of the ERRs with two rings coupled in a point-to-point manner is discussed under two operating conditions. An ERR-based microring modulator shows a high operation speed up to 30 GHz. ERRs with distributed coupling are briefly described as well.