This paper reviews optical structures that utilize mechanism other than the traditional total internal reflection to (quasi-)guide light. Instead, they use the leaky defect-resonance mechanism. Structures with 2-D (i.e. channel waveguides) cross-sections will be studied using a finite element method leaky mode solver. The results will be used to get insights into their properties and principles. Structures being studied include integrated-optical and fiber-optical leaky waveguides, among others are the buffered leaky waveguides, the ARROWs (antiresonant reflecting optical waveguides), and the photonic crystal fibers. Besides structures that guide light in solid materials, we will also discuss structures that guide light in an air core as we...