Contemporary puppetry is the body of work made since roughly the mid twentieth century that treats puppetry as a serious theatrical art form for any audience, rather than as entertainment for children.
The change that made it possible
was abandoning the booth. Once companies accepted that an audience will grant a puppet life even while watching the person operating it, the puppeteer could stand wherever the puppet needed them. Everything else followed from that.
Japanese influence
Western companies encountering bunraku in the twentieth century took two lessons directly: that visible operators disappear, and that multiple performers sharing one figure produce a subtlety no single operator can. Most contemporary ensemble work descends from that encounter.
Object theatre
pushed further, performing with ordinary things — a suitcase, a chair, a pair of gloves — rather than representational figures. The claim is that anything can be given life by attention, and it turns out to be true.
Adult subject matter
Contemporary work handles grief, war, memory and politics, and it has reached large audiences doing it. The horse in War Horse is a three-person tabletop puppet performing for a full theatre of adults.
What it means for a builder
There is no canonical construction. Materials are chosen for what the piece needs — foam, wood, paper, steel, fabric, salvage. The tradition explicitly does not tell you how to build, which is liberating and also means you own every decision.
It has not replaced anything
Traditional forms continue alongside it, and many contemporary artists train in them first. The distinction is one of intent, not of quality or of era.