The 3D conformation of a protein in the space is the main factor which determines its function in living organisms. Due to the huge amount of newly discovered proteins, there is a need for fast and accurate computational methods for retrieving protein structures. Their purpose is to speed up the process of understanding the structure-to-function relationship which is crucial in the development of new drugs. There are many algorithms addressing the problem of protein structure retrieval. In this paper, we present several novel approaches for retrieving protein tertiary structures. We present our voxel-based descriptor. Then we present our protein ray-based descriptors which are applied on the interpolated protein backbone. We introduce five novel wavelet descriptors which perform wavelet transforms on the protein distance matrix. We also propose an efficient algorithm for distance matrix alignment named Matrix Alignment by Sequence Alignment within Sliding Window (MASASW), which has shown as much faster than DALI, CE, and MatAlign. We compared our approaches between themselves and with several existing algorithms, and they generally prove to be fast and accurate. MASASW achieves the highest accuracy. The ray and wavelet-based descriptors as well as MASASW are more accurate than CE.