As of 2020, Proxima Centauri has two confirmed exoplanets: Proxima Centauri b (discovered 2013) and Proxima Centauri c (2019). There are hints of a third, but these are not clear enough to be distinguished from statistical noise. It should be noted that by the common naming convention, Proxima Centauri itself is 'Proxima Centauri a'.
Proxima Centauri b:
Proxima Centauri b orbits close enough to Proxima Centauri that it may have liquid water on its surface. It is only 0.0485 AU (7.5 million km) out, 10 times closer to the star than Mercury is to Sol. However, as Proxima Centauri is a red dwarf, this is about where we expect its Goldilocks zone should be -- with the caveat that Proxima Centauri is a flare star, which may not make the neighborhood healthy for advanced life forms. Additionally, it receives only about 65% of the light from its sun that Earth receives from ours, and most of that is in the infrared spectrum, with only about 3% of the light energy being in the range to support photosynthesis; it also receives high levels of x-ray radiation, about 400 times as much as Earth.
Proxima Centauri b has an orbital period of 11.186 Earth days; its rotational speech and orbital inclination are unknown. Some have speculated that it may be close enough to its star to be tidally locked, or locked in a 3:2 or even 2:1 spin-orbit resonance. We have not yet detected signs of a moon.
If the planet has a strong magnetic field to protect it from the high solar wind that could strip it of its atmosphere, and likewise protect it from the radiation that could kill most known lifeforms, and if it is not tidally locked, it might border on being an Earth-like planet; even if it does not have these features, it is possible that humans could survive in sub-surface habitats. All-in-all, Proxima Centauri b doesn't actually look all that interesting to humans, aside from the fact that it is near to us and may have liquid water, potentially allowing some form of life to arise.
Proxima Centauri c:
Proxima Centauri c orbits at 1.49 AU (220 million km) away from Proxima Centauri, and is probably about seven times as massive as Earth. It orbits the star once every 1,928 days (5.28 Earth years). It is bright for its size, which may indicate a fairly large ring system; if the brightness is due entirely to rings, the rings would extend ~715,000 km in diameter, as compared to Saturn's 270,000 km. Comparatively little is known about this planet, compared to its smaller sibling.
This is a heavy planet, and a cold one. Proxima Centauri is estimated to have a habitable zone of between ∼0.0423–0.0816 AU, making this planet an icy outlier; while it is not large enough to qualify as an ice giant, it is large enough to make landing and then taking off again nearly impossible -- never mind the difficulty of living under seven gravities -- and would not provide any particular benefits as far as human settlements go.
Currently most research into the Proxima Centauri systems involve careful telescopic inspection, but there are some plans to head out that way for a visit. The most well developed of these is probably NASA's 2069 Alpha Centauri mission, which hopes to send a probe to the system. It is not yet funded and will require some technologies that do not yet exist, but NASA has some time yet to get the details sorted.