Humanoid robots, unmanned rovers, entertainment pets, drones, and so on are great examples of mobile robots. They can be distinguished from other robots by their ability to move autonomously, with enough intelligence to react and make decisions based on the perception they receive from the environment. Mobile robots must have some source of input data, some way of decoding that input, and a way of taking actions (including its own motion) to respond to a changing world. The need to sense and adapt to an unknown environment requires a powerful cognition system. Nowadays, there are mobile robots that can walk, run, jump, and so on like their biological counterparts. Several fields of robotics have arisen, such as wheeled mobile robots, legged robots, flying robots, robot vision, artificial intelligence, and so on, which involve different technological areas such as mechanics, electronics, and computer science. In this article, the world of mobile robots is explored including the new trends. These new trends are led by artificial intelligence, autonomous driving, network communication, cooperative work, nanorobotics, friendly human-robot interfaces, safe human-robot interaction, and emotion expression and perception. Furthermore, these news trends are applied to different fields such as medicine, health care, sports, ergonomics, industry, distribution of goods, and service robotics. These tendencies will keep going their evolution in the coming years.