The study of topological superconductivity has been at the forefront of condensed matter physics for the past few years. Topological superconductors are predicted to have odd parity pairing and host so called Majorana fermions, which are not only of fundamental importance, but also proposed to be building blocks for fault-tolerant quantum computing. In this dissertation, we use point contact spectroscopy to study the pairing symmetry of candidate topological superconducting materials. We study proximity induced superconductivity in the topological insulator Bi2Se3 by a superconducting niobium tip, and propose a model to explain its features in point contact spectra. We further study the nature of the superconductivity in highly doped superconducting topological insulators, including CuxBi2Se3 and Sn1-xInxTe, using both a normal metal gold tip and a superconducting niobium tip. For CuxBi2Se3, we observe a robust zero-bias conductance peak (ZBCP) in the differential conductance spectra with the gold point contact, while with the niobium point contact we find the height of the peak exhibiting unusual non-monotonic temperature dependence. We argue that both observations cannot be explained by Andreev reflection within the standard Blonder-Tinkham-Klapwijk (BTK) model, but signify unconventional superconductivity in the material. For Sn1-xInxTe samples, we observe ZBCP in the differential conductance spectra with the gold point contact, while with the niobium point contact, the temperature dependence of ZBCP is monotonic as expected from conventional theory, leaving the nature of the superconductivity of Sn1-xInxTe still an open question.