There's two main sets of losses, as I understand: Resistive losses and radiative losses. You can get into other issues, such as power factor and phase error related losses. The two biggies that hit you almost before you get started are resistive and radiative losses, though, if you just consider a single transmission line driving a resistive load.
You combat resistive losses by going up in voltage, so you can send more power with less current. Since resistive losses are proportional to the square of current, each doubling of voltage reduces your resistive losses by a factor of 4. That's why long haul transmission lines are high voltage.
Radiative losses are different. Whenever you accelerate a charged particle, you generate an electromagnetic wave. With respect to wires carrying current, that corresponds to changing the amount of current. (Current measures the rate at which electrons flow, so changing current means accelerating or decelerating electrons.) That's how radio transmitters works, for example.
In an AC system, that current is continuously changing, so those transmission lines are continuously radiating away some amount energy. But that's not all. If there are any conductors nearby, those E-M waves can induce a current in those conductors, and the resulting E-M waves from that induced current can drag on the AC line further. This mutual induction is how transformers work. But, along an AC transmission line, unwanted coupling results in transmission losses. So, an AC system has a built in, inherent source of losses in the alternating current itself.
In a DC system, with a fixed, perfectly resistive load, the current doesn't change, so there's no radiative losses. In the real world, though, the loading on the system is continually changing, so the actual current demand on the DC system will vary over time, and some energy will be radiated away. To some extent that can be filtered, but that's limited by the amount of storage you can put near the ends of the transmission.
The reason AC won out over DC in the early days is that we didn't have practical means to step DC voltages up and down. But, we had just invented the first practical transformers, and those can step AC to higher and lower voltages trivially.
HVDC is practical now since we've had 100 years to develop better technology for converting DC voltages on the grand scales required.