As the Internet of Things (IoT) concept materialized worldwide in complex ecosystems, the related data security and privacy issues became apparent. While the system elements and their communication paths could be protected individually, generic, ecosystem-wide approaches were sought after as well. On a parallel timeline to IoT, the concept of distributed ledgers and blockchains came into the technological limelight. Blockchains offer many advantageous features in relation to enhanced security, anonymity, increased capacity, and peer-to-peer capabilities. Although blockchain technology can provide IoT with effective and efficient solutions, there are many challenges related to various aspects of integrating these technologies. While security, anonymity/data privacy, and smart contract-related features are apparently advantageous for blockchain technologies (BCT), there are challenges in relation to storage capacity/scalability, resource utilization, transaction rate scalability, predictability, and legal issues. This paper provides a systematic review on state-of-the-art approaches of BCT and IoT integration, specifically in order to solve certain security- and privacy-related issues. The paper first provides a brief overview of BCT and IoT’s basic principles, including their architecture, protocols and consensus algorithms, characteristics, and the challenges of integrating them. Afterwards, it describes the survey methodology, including the search strategy, eligibility criteria, selection results, and characteristics of the included articles. Later, we highlight the findings of this study which illustrates different works that addressed the integration of blockchain technology and IoT to tackle various aspects of privacy and security, which are followed by a categorization of applications that have been investigated with different characteristics, such as their primary information, objective, development level, target application, type of blockchain and platform, consensus algorithm, evaluation environment and metrics, future works or open issues (if any), and further notes for consideration. Furthermore, a detailed discussion of all articles is included from an architectural and operational perspective. Finally, we cover major gaps and future considerations that can be taken into account when integrating blockchain technology with IoT.