Herbal vs Chemical Insecticides
I think you probably mean insect and pest control from plant extracts.  

I have seen posters where extracts from herbs were pretty effective in killing insects.  Really common herbs - rosemary, basi.   It makes sense that plants (and animals) would evolve chemical defenses against insects.  

For instance, a quick search under google scholar talks gives you an idea of the research going on (mostly not in the US) here.  Pestoban, an Indian herbal preparation is quite effective against some pests while less effective (~50% effective) in removing fleas from treated livestock. 

It also stands to reason that the compounds found in edible herbs and plants would tend to be selectively effective against insects found in the environment local to the plants.  

Another related topic is the search for antibiotics in herbs and spices.  Tumeric is a common topic of research, which explains one of the possible reasons its used in cooking. Garlic components show interesting medical properties too. 

While this may seem suspect to some, the research is done in the West too, but it is usually spun a different way. In general if you are looking for bioactive compounds that are not completely toxic (like heavy metals or cyanide for instance), you would want to look at compounds which are made by living things.  Nearly all pharmaceutical designs come from or are derived from plant or microbial / fungal extracts.   This is in fact the field of Natural Products Chemistry which is still a big thing in chemistry and biochemistry.  Few if any of the hot targets of organic synthesis are not some fancy compound found in a plant, fungus or sponge extract.  E.g. the surreally complex Palytoxin, the miracle breast cancer drug Taxol, and the venerable cholesterol control drugs, the Statins.