Robotic manipulation in cluttered environments is one of the challenges roboticists are currently facing. When the objects to handle are delicate fresh fruits, grasping is even more challenging. Detecting and localizing fruits with the accuracy necessary to grasp them is very difficult due to the large variability in the aspect and dimensions of each item. This video proposes a solution that exploits a state-of-the-art neural network and a novel enhanced 6D pose estimation method that integrates the depth map with the neural network output. Even with an accurate localization, grasping fruits with a suitable force to avoid slippage and damage at the same time is another challenge. This video solves this issue by resorting to a grasp controller based on tactile sensing. Depending on the specific application scenario, grasping a fruit might be impossible without colliding with other objects or other fruits. Therefore, a non-prehensile manipulation action is here proposed to push items hindering the grasp of a detected fruit. The pushing from an initial location to a target one is performed by a model predictive controller taking into account the unavoidable delay in the perception and computing pipeline of the robotic system. Experiments with real fresh fruits demonstrate that the overall proposed approach allows a robot to successfully grasp apples in various situations.