Yes, and here are four recent papers on the subject:
1) Evaluation of selected rice accessions for allelopathic potential against Barnyard grass By: Mazid, M. S.; Juraimi, A. S.; Rafii, M. Y.; et al. Volume: 43 Issue: 2 Pages: 159-174 Published: MAR 2018
2) Allelopathic potential of Tridax procumbens L. on radish and identification of allelochemicals By: Andriana, Y.; Xuan, T. D.; Quan, N. V.; et al. Volume: 43 Issue: 2 Pages: 223-237 Published: MAR 2018
3) Allelopathic prospective of Retama raetam L. against the noxious weed Phalaris minor Retz. growing in Triticum aestivum L. fields By: El-Darier, Salama M.; El-Kenany, Eman T.; Abdellatif, Amani A.; et al. Volume: 29 Issue: 1 Pages: 155-163 Published: MAR 2018
4) Explanations for Amaranthus retroflexus growth suppression by cover crops By: Gfeller, Aurelie; Herrera, Juan Manuel; Tschuy, Frederic; et al. Volume: 104 Pages: 11-20 Published: FEB 2018
On the one hand, allelopathy is a natural part of most plant defense systems. Breeding may reduce its effectiveness when people select for other traits. In home garden situations one can even try intercropping to reduce weed problems.
In my own experience with biotests I have observed that allelopathy stunts the growth of weeds yet, does not kill them. Definitely, a worthy approach for weed control in an ecological farming system. On a small scale companion planting of species that produce allelochemicals may be effective to suppress weed populations. I agree with Timothy. Also, keep in mind that the presence of specific weeds in the cultivated field often indicate specific soil conditions. Therefore, focusing on the correction or modification of the soil condition that favored the weed population becomes valuable as well. Ehrenfried Pfeiffer's book: "Weeds and What they tell Us" is an excellent read about this topic.
Phenolic acids and coumarins can be effective in the control of weeds. There efficacy (at least in the laboratory) appears to be maximized in pre-emergence, or in the very early stage of weed growth.
In case of laboratory studies: There are many researches in this field. I have a research showing the effect of camphor and squash plant extracts alone. As well as the effect of mixing the plant extract with herbicides. It shows the importance of selectivity between host plant and grass.
Conference Paper ALLELOPATHIC EFFECTS OF CUCURBITA PEPO L. AND EUCALYPTUS CIT...
Presentation Allelopathic effects of Cucurbita pepo L. and Eucalyptus cit...
With the above mentioned Ph.D thesis
Thesis UTILIZATION OF ALLELOPATHY FOR WEED CONTROL IN CORN "Zea mays L." CROP
The strategy for using allelopathy for weed management could be either through directly exploiting natural allelopathic interactions, especially of crop plants, or applying allelochemicals as a source of natural herbicides.
It depends on the specificity or selectivity of the allelopathic plant to some weed species (target species).
We have published a recent conference paper under the title "Allelopathic effects in species mixtures of legumes".
In this study, we investigated the allelopathic effect of two species of legumes, Alsike clover (Trifolium hybridum; AC) and Black medic (Medicago lupulina; BM), and a mixture (1:1) of the two species. The target weeds were fat-hen (Chenopodium album; FH) and barnyard grass (Echinochloa crus galli; BYG).
We conclude that the allelopathic suppression of root leachates of AC and BM and their mixture on weed reduction is selective. In addition, their autotoxicity and heterotoxicity may affect legume growth itself, and thereby their contribution to sustainable agricultural system performance.
Conference Paper Allelopathic effects in species mixtures of legumes
Yeah. We can use natural plant herbicides to replace chemical herbicides. Of course, the effectiveness depends on the type of extract, the concentration of the extract, and the type of weed.
We can identify, extract and formulate available bioactive compounds so called allelochemicals released by a particular plant(may be crops or weeds) and then using it as a natural herbicides to kill weeds in question...but one constraint behind this concept is lack of broader sense of allelochemical to suppress all the weed species because specific bioactive compound will kill a particular weed only not all the weed species.. mixing of different allelochemicals secreted by different plants may be done in order to ensure its broad-spectrum effect...cold water extract of wheat straw also exhibit allelopathy to kill certain weeds...likewise growing of certain crops either as border crop, nurse crop, intercrop or in definite crop rotation favour allelopathic activities.. certain crops also show inhibitory effect in other crop by secreting chemicals like presence of sunflower in cropping sequence will inhibit growth of lantil, presence of congress grass in the field of maize and sorghum also check growth of these crops...