Although the kinematics and dynamics of spherical robots (SRs) on flat horizontal and inclined 2D surfaces are thoroughly investigated, their rolling behavior on generic 3D terrains has remained unexplored. This paper derives the kinematics equations of the most common SR configurations rolling over 3D surfaces.First, the kinematics equations for a geometrical sphere rolling over a 3D surface are derived along with the characterization of the modeling method. Next, a brief review of current mechanical configurations of SRs is presented as well as a novel classification for SRs based on their kinematics. Then, considering the mechanical constraints of each category, the kinematics equations for each group of SRs are derived.Afterwards, a path tracking method is utilized for a desired 3D trajectory. Finally, simulations are carried out to validate the developed models and the effectiveness of the proposed control scheme. climb obstacles, assuming the condition to be static. From a different view, rolling of SRs are studied where the desired path is assumed to be a straight line with constant slope or a single step obstacle [9-11] and a 2D curved path with variable-slope [12] respectively. In [13], authors have investigated dynamics of Martian tumbleweed rovers while this special type of SR rolls in its heading direction and the turning action is not considered for them. In fact, while several researches have been done on 3D kinematics of other types of mobile robots such as legged [14] and wheeled robots [15,16], to the best of the authors' knowledge, the general problem of kinematics of SRs rolling on 3D terrains has not been investigated in the literature. The motivation to address this problem is that, while many applications of the SRs are on flat surfaces such as indoor [17], and paved roads [18], for a variety of applications such as agriculture [19], surveillance [20], environmental monitoring [21], and even planetary explorations [22], they would get exposed to uneven terrains.In this work, prior to deriving the kinematics of SRs on 3D terrains, a general method for modeling a geometrical sphere rolling over a mathematically known 3D surface is developed. Then, the derived equations are expanded in order to be applied to SRs considering their specifications. Concretely, a variety of mechanisms are utilized in SRs to provide the required propelling torques and forces for their rolling action. Each configuration imposes its own kinematical constraints on the SRs' rolling motion. Therefore, to study the kinematics of SRs it is essential to classify current and feasible designs of SRs accordingly.There are a few SR classifications available in the literature. In a survey [6], SRs are classified based on their mechanical driving principles as: 1) Barycenter offset (BCO), 2) Conservation of angular momentum (COAM), and 3) Shell transformation (OST). In another review, SRs are classified based on their mechanical configurations [23], e.g., single wheel, hamster wheel, pendulum driven, gimbal mechanism, single ball...