As we move into a new decade, the global world of Intelligent Infrastructure (II) services integrated into the Internet of Things (IoT) are at the forefront of technological advancements. With billions of connected devices spanning continents through interconnected networks, security and privacy protection techniques for the emerging II services become a paramount concern. In this paper, an up-to-date privacy method mapping and relevant use cases are surveyed for II services. Particularly, we emphasize on post-quantum cryptography techniques that may (or must when quantum computers become a reality) be used in the future through concrete products, pilots, and projects. The topics presented in this paper are of utmost importance as (1) several recent regulations such as Europe’s General Data Protection Regulation (GDPR) have given privacy a significant place in digital society, and (2) the increase of IoT/II applications and digital services with growing data collection capabilities are introducing new threats and risks on citizens’ privacy. This in-depth survey begins with an overview of security and privacy threats in IoT/IIs. Next, we summarize some selected Privacy-Enhancing Technologies (PETs) suitable for privacy-concerned II services, and then map recent PET schemes based on post-quantum cryptographic primitives which are capable of withstanding quantum computing attacks. This paper also overviews how PETs can be deployed in practical use cases in the scope of IoT/IIs, and maps some current projects, pilots, and products that deal with PETs. A practical case study on the Internet of Vehicles (IoV) is presented to demonstrate how PETs can be applied in reality. Finally, we discuss the main challenges with respect to current PETs and highlight some future directions for developing their post-quantum counterparts.