Needle insertion in soft tissue has attracted considerable attention in recent years due to its application in minimally invasive percutaneous procedures such as biopsies and brachytherapy. This paper presents a survey of the current state of research on needle insertion in soft tissue. It examines the topic from several aspects, e.g. modeling needle insertion forces, modeling tissue deformation and needle deflection during insertion, robot-assisted needle insertion, and the effect of different trajectories on tissue deformation. All studies show that the axial force of a needle during insertion in soft tissue is the summation of different forces distributed along the needle shaft such as stiffness force, frictional force and cutting force. Some studies have modeled these forces. The force data in some procedures is used for identifying tissue layers as the needle is inserted or for path planning. Needle deflection and tissue deformation are major problems for accurate needle insertion and attempts have been made to model them. Using current models several insertion techniques have been developed which are briefly reviewed in this paper.