When you are used to working in the studio, transferring to a live performance is a challenge:
One of the first problems:
The first live processing of acoustic sounds were, of course, done with analogue equipment (Stockhausen, Nono, Cage, etc. some of whose compositions are now rendered with digital processing). For examples the works of Morton Sobotnik from the 60s onward including his idea of a ghost score. Here is a brief description of the idea and an article about these pieces, and an MA thesis about the issues of interaction and performance. Almost 50 years later he is now using the link between Ableton and Max.
The electronic processing does not need to be complex to create interesting results:
But with advances in digital processing the effects applied can be varied and subtle:
You can listen to other examples and explore different ideas about live processing and about interaction.
There is a lively debate about the the meaning of live in live electronics . Composer Natasha Barrett offers one exploration of this topic.