Why are they used?

Analog Switch behaves like a relay, but the switching element is MOSFET transistor. Multiplexers contain multiple switches (typically two, four or eight) depend on the application.

Applications / How do you spot opportunities?

Analog Switches and Multiplexers are used in a wide and growing range of applications include data acquisition, industrial process control, test and measurement, and medical systems as well as signal switching in cell phones, set-top boxes, PDAs, media players, and video games.

How to ask for opportunities?

Do your circuit need switching? What swithcing configuration type need : SPST, SPDT, DPST, DPDT?