Carnivorous plants and sphagnum moss come from the same place, the nutrient-starved acid bog, and they belong together in cultivation. If you grow sundews, pitcher plants, Venus flytraps or butterworts, sphagnum is very likely your main growing medium, and getting it right is most of the battle.
Why sphagnum suits them
Carnivorous plants catch insects precisely because their native bogs offer almost no nutrients in the soil. Pot them in ordinary rich compost and the dissolved minerals scorch their roots and kill them, often within weeks. Sphagnum recreates the bog instead: acidic, extremely low in nutrients, and able to hold water around the roots while still letting air in, which stops them rotting in the constant wet they need. Sundews, the temperate pitcher plants, Venus flytraps and many others grow well in it, alone or cut with lime-free horticultural sand or perlite to open the mix up further.
Live or dried
Both have a place. Dried long-fibre sphagnum, rehydrated, makes a clean, airy potting medium and is what most growers use as the bulk of a mix. Living sphagnum grown over the surface of the pot is even better where you can get it: it keeps the conditions acid, signals the moisture level by its own health, since it pales and shrinks when it dries, and it looks the part. Milled sphagnum, ground fine, is useful for sowing the dust-like seed of many carnivorous plants, since its mild acidity discourages the fungus that damps off seedlings. The wider uses are gathered in sphagnum moss and its many uses.
The water rule
This is the part that catches people out, and it is non-negotiable: water carnivorous plants and their sphagnum only with mineral-free water, meaning rainwater, distilled or reverse-osmosis. Hard tap water steadily loads the medium with the very minerals these plants evolved to do without, and it kills them slowly but surely as the salts build up. They also want no feeding at the roots whatsoever; they feed themselves through their traps, and fertiliser in the pot does harm rather than good. Most are stood in a tray of that pure water through the growing season so the sphagnum stays wet from below, which mimics the bog and saves daily watering.
Keeping the moss and the plants happy
The same conditions serve both. Bright light, high humidity and constant moisture keep the sphagnum lush and the plants growing, and healthy living moss is a fair sign the plant beneath it is content. If the sphagnum starts to brown or thin, look to light and water quality before anything else, since those two account for most trouble. Many temperate carnivorous plants also want a cold winter rest, and the moss simply idles alongside them through it, greening up again in spring. Repot into fresh sphagnum every year or two, since even the best moss eventually breaks down, compacts and loses the open, airy structure the roots depend on.
A note on peat
Traditional carnivorous-plant mixes leaned heavily on peat, which raises the same conservation problem set out in sphagnum, peat and why peat-free matters. Sustainably sourced or cultivated sphagnum, and the growing range of peat-free bog mixes, let you grow these plants well without digging up the very habitat they come from, which is a fitting thing to keep in mind for plants so tied to the bog.