Visual gaze movement is one of the main processes in human interaction with the physical environment, and is a manifestation of the visual perception process. In humans, the interaction of gaze with environment involves mainly three patterns including fixation, smooth pursuit and saccade. This paper investigates two classification techniques to identify gaze patterns: An empirical threshold method and a Hidden Markov Model (HMM). A registration process was initially performed to transform the gaze and environmental visual cues into a common coordinate system, which provides an additional feature to construct gaze models. With the gaze models, the HMM method accurately identifies gaze patterns in gaze trajectories, and in addition enables three types of applications. One is the detailed analysis of visuo-motor control behavior. The second is gaze-mediated teleoperation, showing the real-Time capability of the gaze classification method. The third is the application to surgery tasks, enabling surgical skill analysis.