The sustainable management of the environment and crop production in modern agriculture involves dealing with challenges from climate change, environmental pollution, depletion of natural resources, as well as pressure to cope with dependence on agricultural inputs. Balancing crop productivity with environmental sustainability is one of the main challenges for agriculture worldwide. The emergence of weeds resistant to synthetic herbicides generates huge economic losses, so unconventional weed control strategies, especially those based on ecological principles, are very much needed in modern agriculture. Incorporating a natural eco-friendly approach—allelopathy—as a tool in an integrated weed control plan by growing specific crops or spraying fields with extracts containing allelopathic compounds can significantly reduce the use of herbicides. Allelopathy is considered a multi-dimensional phenomenon occurring constantly in natural and anthropogenic ecosystems, by which one organism produces biochemicals that influence the growth, survival, development, and reproduction of other organisms. The objective of this systematic literature review is to present a comprehensive overview of allelopathy, define this phenomenon, and classify allelochemicals. This paper also discusses and highlights recent advances, ongoing research, and prospects on plant allelopathy management practices applied in agriculture, and the underlying allelopathic mechanisms. The review suggested the holistic view of some allelochemicals as an ecological approach to integrated weed control and is an important contribution to future research directions of multidisciplinary programs, chemoinformatic tools, and novel biotechnology methods to plant breeding.