The Natural History Museum is a new game feature released on Feb 24, 2015. It allows players to assemble fossil skeletons and to revive extinct species. The species currently available can be found under this page; there's also a sheet on the Wiki Spreadsheet.
Click for larger image
The Museum can be built for a whopping 7.25 mil at level 35, or unlocked for 135 diamonds at level 20. Once it's unlocked, you can start sending your paleontologist out to find fossil pieces, which can also be traded. (Note: fossil pieces are Rank 5, which is a brand new level; before this 4 was the highest level!) Paleontologists search for random pieces, unless you pay diamonds to focus them. Skeletons can be placed in your zoo or in the Museum Exhibition building.
Fossil Hunt screen
It takes 10 hours for a paleontologist to return with a fossil piece. It costs $26,000. Additional paleontologist slots can be created:
2nd: $100,000
3rd: 25 diamonds
4th: 50d
5th: 75d
6th: 100d
Paleontologists need a break of 6 hours after returning. You can override the break for 3d, you terrible slave driver.
Creating Animals
You can also revive extinct species with the help of lab techs. They research these new (old) animals by converting fossil pieces into animal pieces. Research can be expedited by clicking the research pins over related species; pins show up pretty frequently and each one takes a who-cares 4 minutes off your research time. Research assistant employees can do this process for you. Whee, Segways!
In order to revive extinct species, you'll need:
1) To have a complete skeleton for that species;
2) To collect more fossil pieces;
3) Each fossil piece can be converted to an animal piece by your lab tech.
So to make one live quagga, you'll need 19 fossil pieces: 5 for the skeleton and then 14 converted into animal pieces for the beast itself. For the dodo, you'll need 27 pieces.
Lab screen
Exhibition area
You can put your fossils and revived animals in the Museum Exhibition area if you don't want them in your main zoo. (You can put other animals there too, if you really want to.) Enclosure house wallpapers will work here. I'm not clear yet on whether zookeepers and gardeners can hit the Museum Exhibition area, but I suspect they can't - which will certainly present problems.
Exhibition area - click to enlarge
Museum Levels
Your museum building can be upgraded.
Level 2: 500 points
Level 3: ? points - Stone Age animals available for what looks like $10 mil, holy Hannah