In this review paper, we are interested in the models and algorithms that allow generic simulation and control of a soft robot. First, we start with a quick overview of modeling approaches for soft robots and available methods for calculating the mechanical compliance, and in particular numerical methods, like real-time Finite Element Method (FEM). We also show how these models can be updated based on sensor data. Then, we are interested in the problem of inverse kinematics, under constraints, with generic solutions without assumption on the robot shape, the type, the placement or the redundancy of the actuators, the material behavior… We are also interested by the use of these models and algorithms in case of contact with the environment. Moreover, we refer to dynamic control algorithms based on mechanical models, allowing for robust control of the positioning of the robot. For each of these aspects, this paper gives a quick overview of the existing methods and a focus on the use of FEM. Finally, we discuss the implementation and our contribution in the field for an open soft robotics research.