I know several applications where twisted pairs are used and why they are used in those applications, but I would like to know more about the advantages and disadvantages of using twisted pair wires so I can choose appropriately based on what I am designing.
As an example, I understand the use of a twisted pair in differential signaling. This helps reduce noise because both wires receive the same interference which can then be removed by a differential amplifier.
I also remember reading quite a while ago about an induction forge where the power output was significantly lower than anticipated. The guy figured out that the separation of the power leads to the electronics enclosed a large area, creating extra inductance (which acted as a low-pass filter decreasing the power factor). By taping the power wires in a bundle, the stray inductance was removed.
It seems that twisted pairs offer benefits when inductance or induction are concerns, but this is where my understanding terminates.
What are the advantages and disadvantages of twisted pairs, and for what applications does this make them beneficial?
EDIT: The issue of inductance does not appear to be addressed elsewhere, indicating one application for which twisted pairs are helpful, which isn't addressed outside this question. Similarly, a comment raised the issue of added capacitance, which is not addressed in the linked question.