Over the years, the Internet has been enriched with new available communication technologies, for both fixed and mobile networks and devices, exhibiting an impressive growth in terms of performance, with steadily increasing available data rates. The Internet research community has kept trying to evolve the transport layer protocols to match the capabilities of modern networks, in order to fully reap the benefits of the new communication technologies. This paper surveys the main novelties related to transport protocols that have been recently proposed, identifying three main research trends: (i) the evolution of congestion control algorithms, to target optimal performance in challenging scenarios, possibly with the application of machine learning techniques; (ii) the proposal of brand new transport protocols, alternative to the Transmission Control Protocol (TCP) and implemented in the user-space; and (iii) the introduction of multipath capabilities at the transport layer.