Topological materials have attracted much attention due to their novel physical properties. These materials can not only serve as a platform for studying the fundamental physics, but also demonstrate a significant potential application in electronics, and they are studied usually in two ways. One is to constantly explore new experimental phenomena and physical problems in existing topological materials, and the other is to predict and discover new topological material systems and carry out synthesis for further studies. In a word, high-quality crystals are very important for studying quantum oscillations, angle resolved photoemission spectra or scanning tunneling microscopy. In this work, the classifications and developments of topological materials, including topological insulators, topological semimetals, and magnetic topological materials, are introduced. As usually employed growth methods in growing topological materials, flux and vapour transport methods are introduced in detail. Other growth methods, such as Bridgman, float-zone, vapour deposition and molecular beam epitaxy methods, are also briefly mentioned. Then the details about the crystal growth of some typical topological materials, including topological insulators/semimetals, high Chern number chiral topological semimetals and magnetic topological materials, are elaborated. Meanwhile, the identification of crystal quality is also briefly introduced, including the analysis of crystal composition and structure, which are greatly important.