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It is widely believed that topological superconductivity, a hitherto elusive phase of quantum matter, can be achieved by inducing superconductivity in topological materials. In search of such topological superconductors, certain topological insulators (like, Bi$_2$Se$_3$) were successfully turned into superconductors by metal-ion (Cu, Pd, Sr, Nb etc. ) intercalation. Superconductivity could be induced in topological materials through applying pressure as well. for example, a pressure-induced superconducting phase was found in the topological insulator Bi$_2$Se$_3$. However, in all such cases, no conclusive signature of topological superconductivity was found. In this review, we will discuss about another novel way of inducing superconductivity in a non-superconducting topological material -- by creating a mesoscopic interface on the material with a non-superconducting, normal metallic tip where the mesoscopic interface becomes superconducting. Such a phase is now known as a tip-induced superconducting (TISC) phase. This was first seen in 2014 on Cd$_3$As$_2$ at IISER Mohali, India. Following that, a large number of other topological materials were shown to display TISC. Since the TISC phase emerges only at a confined region under a mesoscopic point contact, traditional bulk tools for characterizing superconductivity cannot be employed to detect/confirm such a phase. On the other hand, such a point contact geometry is ideal for probing the possible existence of a temperature and magnetic field dependent superconducting energy gap and a temperature and magnetic field dependent critical current. We will review the details of the experimental signatures that can be used to prove the existence of superconductivity even when the "text-book" tests for detecting superconductivity cannot be performed. Then, we will review different systems where a TISC phase could be realized.