Flexible substrates have become essential in order to provide increased flexibility in wearable sensors, including polymers, plastic, paper, textiles and fabrics. This study is to comprehensively summarize the bending capabilities of flexible polymer substrate for general Internet of Things (IoTs) applications. The basic premise is to investigate the flexibility and bending ability of polymer materials as well as their tendency to withstand deformation. We start by providing a chronological order of flexible materials which have been used during the last few decades. In the future, the IoT is expected to support a diverse set of technologies to enable new applications through wireless connectivity. For wearable IoTs, flexibility and bending capabilities of materials are required. This paper provides an overview of some abundantly used polymer substrates and compares their physical, electrical and mechanical properties. It also studies the bending effects on the radiation performance of antenna designs that use polymer substrates. Moreover, we explore a selection of flexible materials for flexible antennas in IoT applications, namely Polyimides (PI), Polyethylene Terephthalate (PET), Polydimethylsiloxane (PDMS), Polytetrafluoroethylene (PTFE), Rogers RT/Duroid and Liquid Crystal Polymer (LCP). The study includes a complete analysis of bending and folding effects on the radiation characteristics such as S-parameters, resonant frequency deviation and the impedance mismatch with feedline of the flexible polymer substrate microstrip antennas. These flexible polymer substrates are useful for future wearable devices and general IoT applications.