The synergy between the cloud and the IoT has emerged largely due to the cloud having attributes which directly benefit the IoT and enable its continued growth. IoT adopting Cloud services has brought new security challenges. In this book chapter, we pursue two main goals: 1) to analyse the different components of Cloud computing and the IoT and 2) to present security and privacy problems that these systems face. We thoroughly investigate current security and privacy preservation solutions that exist in this area, with an eye on the Industrial Internet of Things, discuss open issues and propose future directions