Very low latency and high reliability are two of the main requirements for new applications exploiting 5G networks. This is the case for the remote operation of robots or vehicles, the autonomous interaction of equipment in a factory, autonomous driving and tactile internet applications. Although the TCP/IP stack has been sufficient as the end-to-end solution for most of the history of the Internet, a number of surveys have appeared recently presenting many different methods for managing the end-to-end communication to meet the requirements of various technologies such as that of 5G networks. In this paper, we present a novel classification of the literature focused on new end-to-end solutions and the creation of services towards the support of low latency (1 ms) and high reliability (10-9 error rate) in current and future 5G networks. We specifically highlight how the proposals can be classified according to enabling technologies and the specific method used to achieve success in terms of the latency and reliability. The literature related to end-to-end solutions for reliable low-latency communications are organized according to three main topics: (i) end-to-end protocols that improve communication in terms of latency and reliability, (ii) functionality or technologies implemented on the network to support the current demands, and (iii) application programming interfaces that enhance the correct utilization of those protocols and additional technologies.