This paper presents an efficient and reliable method for predicting crystal structures using evolutionary algorithms combined with ab initio total-energy calculations. The method allows prediction of the most stable and low-energy metastable structures for a given compound under various pressure-temperature conditions without requiring experimental input. It has achieved a high success rate in predicting structures for ionic, covalent, metallic, and molecular compounds with up to 20 atoms per unit cell. The method has resolved several problems in high-pressure crystallography and identified new high-pressure crystal structures, including ε-oxygen, new sulfur phases, and metastable phases of carbon, sulfur, and nitrogen. The success of the method is attributed to its ability to explore the free energy landscape efficiently, identifying the global minimum and other low-energy structures. The method is based on an evolutionary algorithm that does not require prior knowledge of the system's structure and is self-improving, generating increasingly better structures over generations. It is efficient, scalable, and easily parallelizable, making it suitable for systems with up to 40 atoms per unit cell. The method has been implemented in the USPEX code, which uses real numbers to represent lattice vectors and atomic coordinates, enhancing the algorithm's learning ability. USPEX has been successfully applied to predict crystal structures for various materials, including carbon, sulfur, nitrogen, oxygen, hydrogen, and iron, under high pressure. It has also been used to predict the structure of CaCO3 and other compounds, identifying new phases and metastable structures. The method has shown particular success in predicting molecular structures, including ice and urea, despite the challenges posed by their complex and disordered nature. The method is also capable of predicting the stability of structures at high temperatures and pressures, and has been used to study the phase transitions of materials under extreme conditions. The results demonstrate the power of the method in predicting crystal structures and provide valuable insights into the structural chemistry of materials under different conditions.This paper presents an efficient and reliable method for predicting crystal structures using evolutionary algorithms combined with ab initio total-energy calculations. The method allows prediction of the most stable and low-energy metastable structures for a given compound under various pressure-temperature conditions without requiring experimental input. It has achieved a high success rate in predicting structures for ionic, covalent, metallic, and molecular compounds with up to 20 atoms per unit cell. The method has resolved several problems in high-pressure crystallography and identified new high-pressure crystal structures, including ε-oxygen, new sulfur phases, and metastable phases of carbon, sulfur, and nitrogen. The success of the method is attributed to its ability to explore the free energy landscape efficiently, identifying the global minimum and other low-energy structures. The method is based on an evolutionary algorithm that does not require prior knowledge of the system's structure and is self-improving, generating increasingly better structures over generations. It is efficient, scalable, and easily parallelizable, making it suitable for systems with up to 40 atoms per unit cell. The method has been implemented in the USPEX code, which uses real numbers to represent lattice vectors and atomic coordinates, enhancing the algorithm's learning ability. USPEX has been successfully applied to predict crystal structures for various materials, including carbon, sulfur, nitrogen, oxygen, hydrogen, and iron, under high pressure. It has also been used to predict the structure of CaCO3 and other compounds, identifying new phases and metastable structures. The method has shown particular success in predicting molecular structures, including ice and urea, despite the challenges posed by their complex and disordered nature. The method is also capable of predicting the stability of structures at high temperatures and pressures, and has been used to study the phase transitions of materials under extreme conditions. The results demonstrate the power of the method in predicting crystal structures and provide valuable insights into the structural chemistry of materials under different conditions.