I'm confused: Turing machine model vs. interactivity

It seems that introductory material about computability, Turing
machines in particular, is based on an input-output paradigm. That
is, there's a single "function" being "computed", based on a fixed,
pre-determined list of input symbols. The machine reads and.or
rewrites the input symbols, and produces a set of output symbols.

This is understandable historically, since Turing, von Neumann, etc.
were mostly coming at computing with the goal of getting simple
answers to simple questions. (Such as the ballistics trajectories they
computed in WWII on various hardware, or the human computing done with
dozens of workers sitting at desks, passing partial results forward.)

What seems to be missing is the concept of interactivity. That the
next inputs the machine will read could depend on what outputs it has
written out. (i.e., my next query to the computer will depend on the
results it gave to my last query.)

Could someone please point me to literature or terminology that
explains how interactivity like this fits in with all the Turing
machine-style theory?

.

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