Location and trajectory data are routinely collected to generate valuable knowledge about users' pattern behavior. However, releasing location data may jeopardize the privacy of the involved individuals. Differential privacy is a powerful technique that prevents an adversary from inferring the presence or absence of an individual in the original data solely based on the observed data. The first challenge in applying differential privacy in location is that a it usually involves a single user. This shifts the adversary's target to the user's locations instead of presence or absence in the original data. The second challenge is that the inherent correlation between location data, due to people's movement regularity and predictability, gives the adversary an advantage in inferring information about individuals. In this paper, we review the differentially private approaches to tackle these challenges. Our goal is to help newcomers to the field to better understand the state-of-the art by providing a research map that highlights the different challenges in designing differentially private frameworks that tackle the characteristics of location data. We find that in protecting an individual's location privacy, the attention of differential privacy mechanisms shifts to preventing the adversary from inferring the original location based on the observed one. Moreover, we find that the privacy-preserving mechanisms make use of the predictability and regularity of users' movements to design and protect the users' privacy in trajectory data. Finally, we explore how well the presented frameworks succeed in protecting users' locations and trajectories against well-known privacy attacks.