Who performs the TLB shootdown?

I read this SO question describing what a TLB shootdown is. I'm trying to understand if this is an operation performed by the kernel or by the processor or both?

My questions are :-

1. Does a TLB shootdown happen upon context switch? I would assume no, because there is a need to be able to execute multiple processes concurrently on multiprocessor CPUs. Is this assumption correct?
2. When exactly does a TLB shootdown happen?
3. Who performs the actual TLB shootdown? Is it the kernel(if so, where can I find the code that performs the flushing?) or is it the CPU(if so, what triggers the action) or is it both(the kernel executes an instruction which causes an interrupt, which in turns causes the CPU to perform the TLB shootdown)