There are a number of previous posts on the state of .DDS files which is the container format for Direct3D resources (see MSDN for some basics).
The DDS File Format Lives
DDS Update and 10:10:10:2 Problems
DDSWithoutD3DX Sample Update
With the retirement of the D3DX library, the recommended solutions for working with Direct3D 11 textures and .DDS files are now DirectXTex and DirectXTK.
DirectXTK and DirectXTex both support Windows Store apps (a.k.a. Metro style apps) on Windows 8 as well as traditional Win32 desktop applications on Windows 8, Windows 7, and Windows Vista SP2 with the DirectX 11.0 update. There is a version of DDSTextureLoader used by the Windows 8 DirectX samples as well (see the Direct3D resource loading sample).
Update: Both libraries also work on Windows phone and Xbox One.
One of the advantages of using .DDS files is the abiltiy to make use of Direct3D texture compression. The original Direct3D 9 texture compression schemes (DXT1, DXT2/3, DXT4/5) are still supported (now called BC1, BC2, and BC3) and support is required on all Direct3D 11 API compatible hardware including the 9.1, 9.2, and 9.3 feature levels. These schemes are designed for compressing standard three-channel color data with and without an alpha channel. DirectXTex provides the same software compressor that has been in D3DX for many years, with the addition of a few minor improvements through optional control flags.
Feature Level 10.0, 10.1, 11.0, and 11.1 devices also support BC4 and BC5 compression schemes. BC4 is also known as 3DC+ ("ATI1"), and BC5 is known as 3Dc ("ATI2") or "DXN", and both are designed for compressing single-channel or tow-channel textures such as normal maps. DirectXTex provides the same software compressor that was in D3DX10 and D3DX11.
Feature Level 11.0 and 11.1 devices support BC6H and BC7 compression schemes. BC6H is designed for high-dynamic range (HDR) float16 content, while BC7 is a more robust high-quality alternative to the standard BC1-3 schemes for three-channel color data images. Note that BC6H and BC7 decompression is extremely fast with hardware support, but can be expensive to compress. DirectXTex provides the same software compressor available in D3DX11, but a DirectCompute accelerated version is in the BC6HBC7EncoderDecoder sample.
Update: The latest DirectXTex supports both the CPU and DirectCompute compressors.
Here's a handy table of equivalents for replacing legacy D3DX texture related functions.
DirectXTex library, ComputeNormalMap
DDSTextureLoader: CreateDDSTextureFromFileWICTextureLoader: CreateWICTextureFromFile
DirectXTex library (tools), LoadFromXXXFile then CreateShaderResourceView or CreateTexture
DDSTextureLoader: CreateDDSTextureFromMemoryWICTextureLoader: CreateWICTextureFromMemory
DirectXTex library (tools), LoadFromXXXMemory then CreateShaderResourceView or CreateTexture
No direct equivalent, can use Win32 resource functions and then the ‘from memory’ APIs above.
DirectXTex library, GenerateMipMaps and GenerateMipMaps3D
DirectXTex library, GetMetadataFromXXXFile
DirectXTex library, GetMetadataFromXXXMemory
DirectXTex library, Resize, Convert, Compress, Decompress, and/or CopyRectangle
ScreenGrab: SaveDDSTextureToFile or SaveWICTextureToFile
DirectXTex library, CaptureTexture then SaveToXXXFile
DirectXTex library, CaptureTexture then SaveToXXXMemory
Spherical Harmonics Math, SHProjectCubeMap
The legacy DirectX SDK (see Where is the DirectX SDK?) includes the DirectX Texture Viewer tool. This only supports older Direct3D 9 .DDS files and will fail to load any file using the 'DX10' extension or BC4, BC5, BC6H, or BC7. Visual Studio 2012 can view modern .DDS files directly via File / Open / File... (the Image Files filter includes .dds). There is also a 'ddsview' sample available in the DirectXTex package.
Modern Texture Content Pipelines (Gamefest 2011)
Tiled Resources for Xbox 360 and Direct3D 11 (Gamefest 2011)
Block Compression Smorgasbord (Gamefest 2010)
The various video independent hardware vendors (IHVs) have their own texture toolsets as well.
Note that the NVIDIA tools haven't been updated in some time, and are currently missing support for the DX10 header extension, BC6H, and BC7.
Related: Getting Started with Direct3D 11