When applied in some harsh environments (e.g. in poisonous atmosphere or underwater), odor source localization robots are able to perform better than animals without being hurt. During the past three decades, robotic odor source localization has become a popular research field with various algorithms being proposed. These algorithms can be roughly divided into four categories: gradient-based algorithms, bio-inspired algorithms, multi-robot algorithms and probabilistic and map-based algorithms. In this paper, we present a literature review of these four categories and discuss their pros and cons. We also discuss the current trends and some future challenges according to some research papers published in recent years.