In the past two decades, there has been a continuous rise in the deployment of robots fulfilling social roles that expands across various industries such as guides, service providers, and educators. To establish robots as integral allies in daily life, it is essential for them to deliver positive and trustworthy experiences, achieved through seamless and satisfying interactions across diverse modalities and communication channels. In the realm of human-robot interactions, touch plays a pivotal role in facilitating meaningful connections and communication. To delve into the significance of haptic technologies and their impact on interactions between humans and social robots, an exploration of the existing literature is essential, since the research about touch is the most underrepresented between the other communication channels (facial expressions, movements, vocals etc). A systematic literature review has been carried out, identifying 42 articles with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA), related to touch and haptic technologies and interaction between humans and social robots in the twenty years (2001 -2023). The results show the main differences, pros and cons between the materials and technologies that have been primary used so far, the qualitative and quantitative research that links the HRI touch studies with the human emotion and also the types of touch and repeatability of those methods. The study identifies research gaps and outlines future directions, while it serves as a guide for anyone who will be interesting in conducting HRI touch research or build a haptic system for a social robot.