High-order harmonic generation has important applications in ultrafast science. For atoms and symmetric molecules, only odd-order harmonics are emitted as exposed to strong linearly polarized laser fields. For asymmetric molecules, due to symmetry breaking, both odd and even harmonics are emitted. Present studies have showed that odd and even harmonics have different spectral and temporal properties and therefore need to be studied separately. Here, we will introduce the model for describing the generation mechanism of odd versus even harmonics, and the applications of odd-even harmonics in ultrafast science such as probing the structure and dynamics of electrons within asymmetric molecules.