Stick insects are quite interesting and diverse. Ranging from the large and sturdy Heteropteryx to the large and fragile Phobaeticus, here are some pictures and basics and general info! I am not as experienced with them as with Lepidoptera, but I know the basics and have bred some species. So here is some general info.
Phasmatodea are generally masters of camouflage. They are in most cases sexually dimorphic and capable of both sexual reproduction or parthenogenesis in some cases. Pairings and egg laying are usually straightforward, although some species do require soil to lay their eggs (which they “inject” in the substrate using their ovipositor). Other species are capable of launching their eggs away (Extatosoma) or simply dropping them on the floor.
The food varies per species, but generally most of them accept Bramble (Rubus) and some Privet (Ligustrum) or Ivy (Hedera). Eggs can take quite a while to hatch, ranging from weeks to over a year in some cases. Some species have the ability to take flight in adult forms, particulary the smaller and slender males that have larger wings. Some species have colourful wings that they will reveal upon disturbance to scare predators away.
Leaf insects are often unique cases (pictured: my Phyllium giganteum) but they undergo the same care and treatment as most stick insects. Some, but not all, are parthenogenetic.
As you can see, they are quite diverse and beautiful insects! (Below: Phobaeticus serratipes / Up: male and female of Heteropteryx dilatata, adults). Stick insects are hemimetabolous and undergo nymphal stages before developing into sexually mature adults.