Nowadays, ultrasound Doppler imaging is widely used in assessing cardiovascular functions in the human body. However, a major drawback of ultrasonic Doppler methods is that they can provide information on blood flow velocity along the ultrasound beam propagation direction only. Thus, the blood flow velocity is estimated differently depending on the angle between the ultrasound beam and the flow direction. In order to overcome this limitation, there have been many researches devoted to estimating both axial and lateral velocities. The purpose of this article is to survey various two-dimensional velocity estimation methods in the context of Doppler imaging. Some velocity vector estimation methods can also be applied to determine tissue motion as required in elastography. The discussion is mainly concerned with the case of estimating a two-dimensional in-plane velocity vector involving the axial and lateral directions.