Russia and the Peoples Republic of China have the only operational system in place as of now.
Also formerly the ESA when it utilized Russian technology in its ATV (2008 - 2014), and the PRC has this ability due to buying the technology from Russia in the 1990s.
NASA has demonstrated in orbit refuelling and several private companies are vying for the in-space refuelling contracts of other platforms such as satellites.
To be refuelled, the platform has to have this in its design at launch for this to be carried out and the vast majority of space-based platforms were not designed for this.
The only space-based vehicles that were designed for refuelling from the get go were the Soviet space stations Salyut 6, Salyut 7, Mir and the Russian segment of the ISS. Added to that list in the last few years are the Peoples Republic of China spacecraft and space station.
Because the technology is based on Russian-Soviet experience the Chinese system is essentially the same as the current Russian.
https://ntrs.nasa.gov/api/citations/20000121212/downloads/20000121212.pdf
..most modem spacecraft rely on Propellant
Management Devices (PMD) to outflow liquid. Two
main types of PMD have emerged, the screen channel
and the vane device. The screen channel relies on the
surface tension forces of the liquid in a fine pore size
screen to form a barrier to vapor. Vapor cannot enter
the wetted screen until it overcomes the pressure force
created by surface tension. Typically a screen is used as
one side of a hollow channel. Multiple channels are
arranged throughout the tank to maximize contact with
the bulk liquid.
Resupply of storable propellant has been routinely
conducted by the Progress module on Russian space
stations since 1978.
To avoid the problems of phase
separation a flexible membrane separates the liquid
fromthe pressurant gas. Then the liquid can be
transferred by pressurizing the tank without worrying
about ingesting vapor.
Drawbacks of this system
include life of the membrane, weight and an inability
to deal with vapor evolved from the bulk liquid.
Nevertheless the Progress module includes resupply
tanks holding about 870 kg of propellant (two tanks
of nitrogen tetroxide and two of UDMH hydrazine).
High-pressure nitrogen is used as the pressurant. A
compressor is used to lower pressure in the receiver
tank by transferring nitrogen back into high-pressure
storage bottles.
After the lines have been leak checked
the fuel then oxidizer are transferred one at a time to the
station. Separate transfer for each reduces the hazard in
case of a leak. The process can be controlled either by a
ground station or the space station crew.
This module
and system where first used on Saylut 6 on Jan 20,
1978 and have been used on every space station since
including Mir, and ISS.
ISS had its first refueling
August 2000.
As the propellants used are highly toxic the piping for these are on the outside, so there’s no risk to the crew inside if the pipes leak, but they do come together in the docking collar or ring.
Russian Progress Система стыковки и внутреннего перехода, that contains extra ducts for refuelling propellants. The PRC system is essentially the same.


From this diagram you can see the system is simple - tanks have fuel, introduce nitrogen gas to displace the fuel, moving the bellows through the tank. Fuel is forced out of the tank along its only exit, the pipeline to receiving tank, where in reverse, the bellows are pushed back by the incoming fuel. Piping for this on the Russian station modules are also external, in this way Progress refuels Zvezda SM and Zarya directly, the latter now used as extra fuel storage, and Progress can refuel via Prichal and Nauka MLM and through Poisk (and previously Pirs).

- Delivered fuel components:
- fuel - asymmetric dimethylhydrazine from 62 to 310 kg;
- oxidizer - nitrogen tetra oxide from 112 to 560 kg;
- gas for pressurizing tanks; for checking tightness and purging pipelines - nitrogen is stored in six cylinders (37 ± 2 kg);
SD provides the supply of each fuel component with a flow rate of up to 0.30 l/ s to the DPO subsystem of the ship's CDU (for simultaneous operation of up to 12 DPO) and with a flow rate of up to 0.22 l/ s to the station's ODE. At the same time, the pressure of the fuel components at the entrances to PDPO and in hydraulic connectors of the StA - from 14 to 21 kgf / cm2.
The temperature of the refuelling system tanks and highways is from 0 to +30


This is Poisk, Pirs was similar (though it lacked scientific payload interfaces, and was replaced by Nauka MLM), a combined airlock, storage and fuel transfer control module. The pumping and control assembly, to transfer fuel from docked Progress supply craft to either Zvezda or Zarya fuel tanks is identified here (Refuelling hydraulic valves), and is covered by an external box, seen above the airlock hatch.
Simple graphic showing Progress refueling a Soviet space station:

.
Peoples Republic of China:
Note, for the PRC, in buying off the shelf technology from Russia in the 1990s, they chose to go the route of APAS (likely to be APAS-89), though they bought technology for the standard probe and drogue system as well (as well as space suits, life support systems, space station module remote docking systems, etc - PRC typically insists on 80 per cent flight-proven technology to reduce chance of failure).
With that they also inherited the refuelling capabilities.
Note below the APAS type system employed in their space craft and space station:

2017: PRC’s first cargo spacecraft, Tianzhou-1, performed the first auto-docking with Tiangong-2 space lab on April 22, followed by the two spacecraft completing their first in-orbit refuelling on April 27.
Refuelling is a 29-step procedure to complete and lasts for several days each time. Key steps such as leak detection of the replenishment pipeline, gas recovery of the storage tank, propellant transportation, and propellant blowing are carried out.

Tianzhou has eight 230-liter propellant tanks holding roughly two metric tons of Monomethylhydrazine fuel and Nitrogen Tetroxide Oxidizer – over half of which was transferred to Tiangong-2 while the rest is retained in a unified propellant system that allows for a maximum of propellant to be transferred to the station module as opposed to the Russian-Soviet system with separate tanks.
Four lines carrying fuel, oxidizer and helium pressurization gas run from the propellant storage to the forward end of the spacecraft where four fluid interfaces are located as part of China’s version (second generation, first lacked refuelling) of the APAS docking system.
Upon formation of the hard-mate between Tianzhou and its target vehicle, the interfaces form a pressure-tight seal that allows propellants to be forced into the partially empty tanks of the space station via a pressure differential. At the end of the refuelling operation, the lines are purged and the interfaces separate as the visiting cargo craft undocks.
PRC display of fuel line pathways:

APAS connectors - fuel transfer points indicated:

Nitrogen Tetroxide Oxidizer connectors, main and back up on the left.
Monomethylhydrazine fuel connectors, main and backup, on the right.
Edit:
The future:
https://www.lockheedmartin.com/en-us/news/features/2021/refueling-satellites-in-space.html
Lockheed Martin is adding another tool to its innovative workbox of pioneering on-orbit satellite servicing capabilities with an investment in Orbit Fab’s Gas Stations in Space refueling technology.
Orbit Fab, a San Francisco-based space-industry startup, has developed end-to-end refueling service using its Rapidly Attachable Fluid Transfer Interface (RAFTI). RAFTI, Orbit Fab’s first product, is a fueling port to allow satellites to be refueled easily in orbit. It can also be used as a drop-in replacement for existing satellite fill-and-drain valves.
Refueling Satellites Subject of STS-135 Experiment
Robotic Refueling Mission (RRM) Experiment will be demonstrated by space shuttle Atlantis and her STS-135 crew
Refuelling Satellites with Robots
https://phys.org/news/2021-09-gas-station-space.html
More on Orbit Fab.
https://phys.org/news/2021-05-nasa-on-orbit-osam-mission-ready.html
NASA's On-orbit Servicing, Assembly, and Manufacturing 1 (OSAM-1) mission ready for spacecraft build
OSAM-1 will, for the first time ever, robotically refuel a U.S. government satellite not designed to be serviced.
https://baike.sogou.com/v85424686.htm
https://spaceflight101.com/tiangong-2/tianzhou-1-completes-2nd-in-orbit-refueling-demonstration-ahead-of-departing-tiangong-2/