Forward, Inverse Search
Forward and inverse search are well-supported by Kile and kdvi, but you need to configure kdvi and Kile as described on the following page:
A short summary:
kdvi: Go to menu Settings -> Configure KDVI -> DVI Specials. There, select [Editor]: Kile
Kile: Go to menu Settings -> Configure Kile... -> Tools -> Build -> LateX. There, change [Select a Configuration]: Modern, and add -src-special=cr,display,hbox,math,par,vbox to the [Options] field, so that it looks like this:
-src -src-special=cr,display,hbox,math,par,vbox -interaction=nonstopmode '%source'.
After you have configured Kile and kdvi correctly, pressing 'ForwardDVI' in Kile displays the currently edited text in kdvi. In kdvi, clicking with your middle mouse button somewhere in your document places the cursor in Kile right at the text you clicked on.