In the Internet of Things era, an increasing number of household devices and everyday objects are able to send to and retrieve information from the Internet, offering innovative services to the user. However, most of these devices provide only smartphone or web interfaces to control the IoT object properties and functions. As a result, generally, the interaction is disconnected from the physical world, decreasing the user experience and increasing the risk of isolating the user in digital bubbles. We argue that tangible interaction can counteract this trend and this paper discusses the potential benefits and the still open challenges of tangible interaction applied to the Internet of Things. To underline this need, we introduce the term Internet of Tangible Things. In the article, after an analysis of current open challenges for Human-Computer Interaction in IoT, we summarize current trends in tangible interaction and extrapolate eight tangible interaction properties that could be exploited for designing novel interactions with IoT objects. Through a systematic literature review of tangible interaction applied to IoT, we show what has been already explored in the systems that pioneered the field and the future explorations that still have to be conducted.