The adoption of network traffic encryption is continually growing. Popular applications use encryption protocols to secure communications and protect the privacy of users. In addition, a large portion of malware is spread through the network traffic taking advantage of encryption protocols to hide its presence and activity. Entering into the era of completely encrypted communications over the Internet, we must rapidly start reviewing the state-of-the-art in the wide domain of network traffic analysis and inspection, to conclude if traditional traffic processing systems will be able to seamlessly adapt to the upcoming full adoption of network encryption. In this survey, we examine the literature that deals with network traffic analysis and inspection after the ascent of encryption in communication channels. We notice that the research community has already started proposing solutions on how to perform inspection even when the network traffic is encrypted and we demonstrate and review these works. In addition, we present the techniques and methods that these works use and their limitations. Finally, we examine the countermeasures that have been proposed in the literature in order to circumvent traffic analysis techniques that aim to harm user privacy.