Feedstock recycling of plastic waste by thermal and catalytic processes is a promising route to eliminate this refuse (which is harmful to the environment) by obtaining, at the same time, products that are useful as fuels or chemicals. During the past decade, this option has undergone an important evolution from a promising, scientific idea to an alternative that is very close to reality with commercial opportunities. Thus, several commercial processes have been developed worldwide, most of them especially addressed toward the preparation of diesel fuel. The present review highlights the most remarkable achievements of the field, providing a fundamental insight into this fascinating area and highlighting the main milestones that should be achieved in the next future for this alternative to become applied commercially on a large scale.