We will consider the following 4 methods used for texture compression: 

• Vector Quantization 
• Palletizing 
• Block Decomposition 
• DCTransform 

Vector quantization used by PowerVR in their graphic HW.  Palletizing is usually supported by all graphic HW. S3's S3TC method is based on Block Decomposition. It's used in Savage HW and licensed by Microsoft for DX6. TREC is DCT (JPEG-like) Microsoft solution proposed for standardization.