Invasive techniques actively modify the system in a permanent way.
The “professional” mid range solution. Typically some form of Nd:YAG, either the fundamental or some harmonic. Expect minimum of a few thousand USD for a system, probably many more. Probably the most economical would be to piece together a Mitutoyo microscope. Of course, be careful not to look into your home spun laser while firing without good reason.
The “professional” high end solution used for small processes. Equipment is rather expensive. Some estimates seem to put them around an order of magnitude of 500,000 USD.
FIB time can often be rented on an hourly basis from universities and research labs.
azonenberg is beginning to experiment with FIB. Lab notes
Microprobes can cut traces by moving back and forth. Professional units use peizo's (ie ultrasound).
By masking the chip and then etching (ex: with HF) wires can be removed. Masking compounds range from photoresists to nail polish.
Usually done with a fib. Can be done temporarily with microprobes or possibly on a high process chip very carefully with conductive epoxy.
JM's highlights from watching the presentation
exposing wires
fuses
op amp vs ttl amp for gain
fib probing
anti-anti-re
future/upcoming anti-re
No mention of masked etching. Ex: putting PR or nail polish and etching with HF