Human dexterity is an invaluable capability for precise manipulation of objects in complex tasks. The capability of robots to similarly grasp and perform in-hand manipulation of objects is critical for their use in the ever changing human environment, and for their ability to replace manpower. In recent decades, significant effort has been put in order to enable in-hand manipulation capabilities to robotic systems. Initial robotic manipulators followed carefully programmed paths, while later attempts provided a solution based on analytical modeling of motion and contact. However, these have failed to provide practical solutions due to inability to cope with complex environments and uncertainties. Therefore, the effort has shifted to learning-based approaches where data is collected from the real world or through a simulation, during repeated attempts to complete various tasks. The vast majority of learning approaches focused on learning data-based models that describe the system to some extent or Reinforcement Learning (RL). RL, in particular, has seen growing interest due to the remarkable ability to generate solutions to problems with minimal human guidance. In this survey paper, we track the developments of learning approaches for in-hand manipulations and, explore the challenges and opportunities. This survey is designed both as an introduction for novices in the field with a glossary of terms as well as a guide of novel advances for advanced practitioners.