Building and maintaining a silicon foundry is a costly endeavor that requires substantial financial investment. From this scenario, the semiconductor business has largely shifted to a fabless model where the Integrated Circuit supply chain is globalized but potentially untrusted. In recent years, several hardware obfuscation techniques have emerged to thwart hardware security threats related to untrusted IC fabrication. Reconfigurable-based obfuscation schemes have shown great promise of security against state-of-the-art attacks -- these are techniques that rely on the transformation of static logic configurable elements such as Look Up Tables (LUTs). This survey provides a comprehensive analysis of reconfigurable-based obfuscation techniques, evaluating their overheads and enumerating their effectiveness against all known attacks. The techniques are also classified based on different factors, including the technology used, element type, and IP type. Additionally, we present a discussion on the advantages of reconfigurable-based obfuscation techniques when compared to Logic Locking techniques and the challenges associated with evaluating these techniques on hardware, primarily due to the lack of tapeouts. The survey's findings are essential for researchers interested in hardware obfuscation and future trends in this area.