Your main responsibilities are:
1. Do what the artist wants.
2. Get the best sound in the hall you can with the equipment available.

As a subsidiary to these, you are typically an advisor to the venue (or the artist if you are traveling with them) regarding the appropriate equipment necessary for providing a quality aural experience for the audience. This means, if you are engineer for a venue, carefully reading the sound riders for a visiting artist, being certain that you will have the equipment requested available or, if not, being certain that the artist has approved whatever modifications you suggest. If you are traveling sound engineer for an artist, this means making certain that a complete, detailed sound rider is made available to all venues well before the performance, and making yourself available to discuss these with a representative of the venue.

Sometimes 1 and 2 above are not totally compatible, in which case you must trade-off some of the artists desires with what you feel is best for the audience. The most difficult part of this typically involves the potential conflict between the artists desire for monitor sound and the potential for this to cause difficulties with sound in the hall. In general though, most artists would agree that you have responsibility for sound in the hall, and they won't try to control it but rather give you suggestions.