The representation of the environment strongly affects how robots can move and interact with it. This paper presents an online approach for continuous mapping using Gaussian Process Implicit Surfaces (GPISs). Compared with grid-based methods, GPIS better utilizes sparse measurements to represent the world seamlessly. It provides direct access to the signed-distance function (SDF) and its derivatives which are invaluable for other robotic tasks and it incorporates uncertainty in the sensor measurements. Our approach incrementally and efficiently updates GPIS by employing a regressor on observations and a spatial tree structure. The effectiveness of the suggested approach is demonstrated using simulations and real world 2D/3D data.