The core Wine development aims at a correct implementation of the Windows API as a whole. Today it's widely used, very popular and sponsored by companies such as CodeWeavers and Valve.
Wine is almost as old as the Linux project, starting in the summer of 1993. Since late 2017 there is also an experimental build for Android. Additionally, compatibility layers may also use emulation in order to run software built for a different architecture. In theory, this should allow for near-native performance since no processor emulation takes place, but in practice some software such as games will tend to run a bit slower due to other bottlenecks that occur as a result of replicating the correct behavior, such as accounting for graphics APIs like Direct3D that aren't supported on non-Microsoft platforms. While not strictly emulation per se (hence why Wine stands for 'Wine Is Not an Emulator'), compatibility layers allow software written for one operating system to run on a different OS, often by translating API and system calls made by an application to their equivalent calls in the host operating system.