DC-AC and DC-DC are just conversions - conversions used to be the problem with DC for distribution. For HVDC in an AC net you need AC-DC (not much of a problem)

DC-AC and DC-DC are just conversions - conversions used to be the problem with DC for distribution. For HVDC in an AC net you need AC-DC (not much of a problem) and DC-AC (more difficult, solved with only minor losses today). The advantages of DC transmission are flexibility (can have power flow either way between any unsynchronized AC nets) and lower transmission losses per distance. The details are all on Wikipedia.