HVDC is used for long-distance transmission where taps aren't necessary, and to connect disparate AC standards. Popular applications are undersea cables, remote generation facilities, and intercontinental or inter-country distribution. It's a lot more efficient than AC over distance as it requires fewer conductors and doesn't suffer from skin effect, so transmission losses are lower. And since you're already doing the AC->DC->AC conversion, there's no need for the connected grids to be synchronized.
As renewables (solar, wind, hydro) become more popular, so too does the need for reliable long-distance power transmission. With fossil fuel, fuels could be delivered to the point of generation - with solar, wind, and hydro, the location of the generator is non-negotiable and so the energy must be transported instead.
So we'll probably see more and more HVDC systems in coming years.
For undersea connections, the water around it means the line has a lot higher capacitance. An AC link has to load/unload that capacity all the time and looses energy to it, a DC link doesn't.
Similar effects happen with normal power lines as well, so it also has benefits on long-distance connections on land. Since you need conversion equipment on all ends, it's typically used only for point-to-point links, not for lines with branches in between - an example might be connection hydro plants in the wilderness somewhere to more populated areas.
For links between non-synchronized networks, since conversion is needed anyways to match between them.
HVDC is becoming more common for medium and long distance transmission lines because HVDC doesn't suffer from the "skin effect" where current is carried mostly by the outside of the conductor, and therefore you can transmit more power with less conductor with HVDC. The tradeoff is, it's much easier to step up and step down AC voltage (using solid state transformers)
The recent change is the fact that high-voltage semiconductors now make step-up/step-down efficient. In many cases, more efficient than purely using transformers (most semiconductor stuff still uses some form of inductive effect--they just do so at MUCH higher frequencies than in the past which allows them to use MUCH smaller components and get much higher efficiencies).
One of the big advantages of AC has to do with switching. If you flip a switch on AC, within about 10 milliseconds the voltage goes to zero as a natural consequence of the waveform irrespective of what current was flowing previously. A switch can interrupt that without much grief.
If you flip a switch on DC, it has to completely stop the current flow in the presence of a large current and/or voltage that will create a conductive plasma. That means a much larger switch for the same level of power.
There is a reason why your ISP has a huge switch and it is often encased in some inert gas. And also why it sounds like a bomb going off if it trips. And why it takes a hydraulic pump to reset.
Side note: The Pacific DC Intertie was the largest in the world until the 3 Gorges Dam interties--and it dated to the Kennedy administration and used vacuum tubes.
https://en.wikipedia.org/wiki/Pacific_DC_Intertie
In Europe you start to see some projects like that to connect renewable energy sources to consumption areas. The last notable one has a 1.4GW capacity[0] between France and Spain.
I have not heard much about long-distance DC lines in the United States, where AC transmission lines are incredibly common. However, I have read long-distance DC transmission lines are becoming more popular with alternative energy sources in China, such as the Three Gorges Dam project.
My understanding is that the vast majority of power infrastructure is AC, and long distances are using High Voltage AC lines