G-quadruplexes (GQs) are secondary nucleic acid structures that play regulatory roles in various cellular processes. G-quadruplex-forming sequences present within the 5′ UTR of mRNAs can function not only as repressors of translation but also as elements required for optimum function. Based upon previous reports, the majority of the 5′ UTR GQ structures inhibit translation, presumably by blocking the ribosome scanning process that is essential for detection of the initiation codon. However, there are certain mRNAs containing GQs that have been identified as positive regulators of translation, as they are needed for translation initiation. While most cellular mRNAs utilize the 5′ cap structure to undergo cap-dependent translation initiation, many rely on cap-independent translation under certain conditions in which the cap-dependent initiation mechanism is not viable or slowed down, for example, during development, under stress and in many diseases. Cap-independent translation mainly occurs via Internal Ribosomal Entry Sites (IRESs) that are located in the 5′ UTR of mRNAs and are equipped with structural features that can recruit the ribosome or other factors to initiate translation without the need for a 5′ cap. In this review, we will focus only on the role of RNA GQs present in the 5′ UTR of mRNAs, where they play a critical role in translation initiation, and discuss the potential mechanism of this phenomenon, which is yet to be fully delineated.