Most tutorials dont go father than how to emit a basic billboard particle.
Because that's all there is to it. Just smoke and mirrors.
The key is in a good system that can emit lots of controlled billboards. And by "controlled" it means how many particles are emitted per second, of which type (i.e. size, material), rate of growth per second, colour randomization, where do they get emitted, if they follow a predetermined path or are attracted by some force (like gravity) etc.
The rest is just really good artists knowing how to take advantage of it.
Google "particle system emitter affector" for ideas on how to implement your own (i.e. a quick google returns these interesting links)
There are a few exceptions though i.e. for thunder/lightning effects you're better off writing a code that will create a chain/path of connected billboards (each billboard slightly reoriented) that randomly split into 2 or 3 paths at certain points. Then repeat until desired length is reached. (like this, but in 3D)
When we mean "advanced particle effects" we actually mean about voxels, fluids, and other very compute intensive stuff which isn't what you're asking for.