Blaberus spp.

Housing:

Smaller species could be started off in containers as small as 1-2 gallons, but for larger species and large colonies, enclosures in the 5-10 gallon range are recommended. Moderate to high ventilation is advised. A substrate of coconut fiber, sphagnum peat, potting soil, etc. at least an inch or two deep is recommended for most species, though some of the common feeder species like discoidalis and "fusca" can be bred perfectly fine with no substrate at all (though they probably prefer having some substrate). Most species do well with a 50/50 horizontal humidity gradient, one half of the enclosure kept humid, the other half dry. Exact humid preferences differ between species, but in general this is a good place to start.

Hides in the form of cardboard tubes, eggcrate, vertically slanted bark, and plywood "roach-huts" should be provided. Most Blaberus species are burrowers as nymphs, and often as adults, but the adults of the brasilianus and giganteus species groups prefer having vertically slanted hides above ground, and often need such surfaces to molt to adulthood successfully in the first place. Nymphs of all Blaberus will also take advantage of above ground hides sometimes as well, so it's never a bad idea to offer them.

Diet:

A staple diet of dog/cat/fish/chick feed, along with fruits and veggies works just fine for all these species. Some of the more picky ones may also benefit from having leaf litter added to their diet.

Temperature: 

Temps in the 75-85F° range are recommended for optimal growth and breeding. Some species will breed at lower temps though, albeit at a slower rate.

Breeding/Life Cycle:

Adults typically live 1-2 years depending on the species, and the nymphs take 4-8 months to mature depending on species and temperatures. Gestation should only take 2-4 months under optimal conditions, and females of this genus typically give birth to 20-30 offspring per litter.

Most are pretty hardy when it comes to lapses in care, and can be quite resilient against most common pests. By far the most destructive pests to this genus are phorid flies, which feed on dead roach bodies and will sometimes attack stressed live roaches. Thus, dead roach bodies should be regularly removed from enclosures so as to prevent phorid fly numbers from getting out of control. 

Cleaner crews such as dermestid beetles and lesser mealworms can work well for eating dead roach bodies, though both can cause problems of their own if their numbers aren't kept in check, so keep that in mind.

Species within the same species groups of this genus CAN AND WILL hybridize, and sadly many hybrids have been created accidentally in the pet/feeder hobby, almost always mislabeled and sold under pure species names... Be careful where you source your Blaberus species, as not only do hybrid Blaberus often look less pretty than their pure bred counterparts, but some hybrid strains breed quite poorly too and aren't even very suitable as feeder stock.

Now, for some specific notes for each of the species currently in the hobby:

(Species group atropos)

Blaberus atropos:

This species is perhaps one and the same with discoidalis, the main difference is the commonly cultured atropos strains seem to have more pronotum pattern variation than is typically seen in pure discoidalis strains. A hardy species nonetheless that likes to burrow, and is quite prolific.

Blaberus boliviensis:

Another chunky species that likes to burrow, as is the norm for this species group. They are rather unique in patterning, with a large black spot in the middle of their pronotum, often with two red dots inside. A lot of captive stock is hybridized with other members of this genus, so be careful where you get them from.

Blaberus discoidalis:

One of the most common feeder roach species, or at least they used to be. Nowadays a large portion of "discoidalis" sold on the market are hybrids, and often not even hybrids with actual discoidalis!

This species does well when kept quite dry, but isn't picky about humidity. They will burrow a lot when given a substrate, but can be reared in a bare bottom enclosure with eggcrate hides too in traditional feeder fashion.

Blaberus parabolicus:

This species is quite large for this species group, and super hefty to boot. This species is a bit slower growing than the other species in this group, but quite prolific once they get breeding. As usual for this species group, they love burrowing.

Blaberus sp. "Venezuela":

There is some debate as to whether these are merely a strain of discoidalis, or even a hybrid strain... However they've been in culture for a very long time and have two consistent color forms, adults with a black spot in the middle of their pronotum, and adults with a reddish brown spot instead. Not a picky species, like the others in this group they enjoy a substrate for burrowing and aren't very picky about humidity. Can be a bit slower breeding at times, but they are quite hardy.

(Species group brasilianus)

Blaberus colosseus:

This is a large species with three distinct strains in the hobby from Ecuador, Panama and Peru. The three strains have similar care, and enjoy relatively dry conditions, with a quarter to a third of the enclosure kept humid. This species greatly appreciates lots of vertically slanted wood/bark hides for the adults, and being such a large species needs an ample amount of room to breed well. Constant food availability is a must as well, especially of being kept warm. Adult males can be quite territorial and can fight with each other in cramped conditions. They can be a bit finicky at times, and sometimes females will just withhold broods for seemingly no reason.

Blaberus cf. chacoensis "Pantanal, Brazil":

A very hefty, chunky species that enjoy burrowing. Unique in patterning and morphology from all other hobby Blaberus spp.. Fairly finicky compared to some of the other Blaberus spp., with cultures randomly crashing and refusing to reproduce for some keepers. 

(Species group giganteus)

Blaberus craniifer:

There are three distinct strains of this species (the dark-winged form at least) in the hobby, "UCR" "Orin's", and "Euro". This species does well under a variety of conditions, isn't too picky about humidity and is very hardy. All life stages will burrow but do like having vertical hides available for the final molt to adulthood, and for the adults to climb on.

Blaberus sp. "fusca":

Honestly probably a lighter winged form of craniifer. "fusca" isn't even a valid species name and is a synonym for B.atropos, though this strain definitely isn't even in that species complex. In any case, pure stock of this strain (which can be hard to find) is very hardy and in a variety of conditions, so they're often used as feeders. Whether you use substrate or not, vertical hides for the adults are recommended.

Blaberus giganteus:

Old hobby stock of this species can be finicky at times, considering these are THE largest Blaberus species, they need a LOT of space, and they prefer humid but well ventilated conditions. Some say a good, organically rich substrate is key to breeding this species, and others have no problem just using plain coco fiber... But all seem to agree that lots of vertical hides for the adults and for the nymphs to molt to adulthood from are very important. Adult males can be quite territorial and will rip each other to shreds in crowded conditions or in simply male heavy colonies. Steady heat and fresh fruits can help induce breeding, and when kept optimally this species can actually be quite prolific.

Blaberus giganteus "Honduras":

There is quite the debate as to the identity of this species, and they may actually be undescribed, but as it stands right now they key out to giganteus IMO, and probably are a geographic variation of that species. In any case, they've proven way hardier and less picky than the older giganteus stocks, and are darker in coloration. They do prefer high humidity and good ventilation, lots of space, vertical hides, etc., but aren't as prone to crashes or quite as demanding as normal giganteus.

Blaberus sp. "peruvianus":

Another old strain that may just be a light winged form of craniifer, as they're capable of hybridizing with craniifer and "fusca" (and thus lots of hybrids are sold under the "peruvianus" name). Real B.peruvianus belong in the atropos species group, whereas these hobby "peruvianus" do not look like they belong to that species group at all, which further proves they are likely misidentified. Whatever they may be, this strain can be cared for in much the same way as craniifer/"fusca", and overall is quite hardy.