When cages or aquaria are constructed from acrylic the panels are solvent welded together. You use a fairly low-viscosity solvent that is injected along edge-joints with a syringe. The solvent softens the acrylic up and the two pieces essentially melt/weld together as the solvents evaporate. Similar process as joining PVC pipe.
Solvent welding plastics is not terribly difficult but acrylic itself has a pretty steep learning curve. The edges really need to be perfectly prepared for best success. A high speed router with an acrylic-specific bit is the best way to do this.
Acrylic is also not idea for all herp applications. It is very susceptible to warping in particular. But in the right hands and in the right situation it is great.