Pushing actions are common mechanisms present in most human and industry manipulations. Nevertheless, finding a precise description for the motion of pushed objects is still an open problem. In this work, we will develop the first data-driven models that can describe the pushing motion taking into account its uncertainty. We will also explain how we collected a high-quality data set for pushing using real experiments that will be available online to motivate research in the pushing domain. A key challenge to describe pushing is understanding friction properly. In most situations, friction makes systems stochastic and introduces uncertainty in our predictions. Moreover, in robot applications, sensors can also add noise into our observations making our state-estimations uncertain. In consequence, our work will consider probabilistic algorithms such as Gaussian Processes to introduce for the first time the uncertainty of our system into the modeling of pushing.