Where at least the following apply, somewhat following upon Bald Bear's answer:

Complex novel/unanticipated situations can be expected to occur, even rarely.

Tasks occuring under highly varying conditions, where compensation strategies are not easy to automate.

Any tasks not comprehensively & reliably addressed via script.

Short of advanced AI, robots are best used for rote tasks or remotely guided.

Where at least the following apply, somewhat following upon Bald Bear's answer:

Complex novel/unanticipated situations can be expected to occur, even rarely.

Tasks occuring under highly varying conditions, where compensation strategies are not easy to automate.

Any tasks not comprehensively & reliably addressed via script.

Short of advanced AI, robots are best used for rote tasks or remotely guided.

EDIT: As HMI sophistication evolves, especially including sensory input, the utility of remote bots increases significantly. This probably happens more readily than AI evolution, since the technological hurdles are far less difficult, less expensive to develop.