High-order harmonic generation (HHG) is a highly nonlinear phenomenon that produces a numerous orders of harmonics. The generated harmonic orders can range from tens to several hundreds, depending on the ionization potential of the target medium and the intensity of the laser. The high harmonics generate a broad spectrum that is evenly distributed in frequency, enabling the production of extremely short light pulses within the attosecond time range. This article provides a brief overview of the key mechanisms involved in high-order harmonic generation from both gaseous mediums and condensed matters.