Opportunities for the valorisation of agro-industrial residues of the chestnut (Castanea sativa Mill.) production chain have been fostered with the production of multifunctional polyphenol-rich extracts with the potential to be introduced as natural additives or active components in several products. Nonetheless, it is crucial to explore the feasibility of different extracts from the various by-products for these applications through the exhaustive study of their composition and bioactivities without losing sight of the sustainable character of the process. This work aimed at the screening of the phenolic compound composition and bioactivities of different green extracts of chestnut burs, shells and leaves, as the first step to establish their potential application as natural ingredients, primarily as food preservatives. To this end, maceration (MAC) as a conventional extraction method besides ultrasound and microwave-assisted extractions (UAE and MAE) was employed to obtain the extracts from chestnut by-products using water (W) and hydroethanolic solution (HE) as solvents. Phenolic compounds were analysed by HPLC-DAD-(ESI-)MS/MS; the antioxidant capacity was assessed by colourimetric assays, and the antimicrobial activity was evaluated against several strains of food-borne bacteria and fungi. The leaf extracts obtained by MAC-HE and UAE-HE presented the highest concentration of phenolic compounds (70.92 ± 2.72 and 53.97 ± 2.41 mg.g−1 extract dw, respectively), whereas, for burs and shells, the highest recovery of total phenolic compounds was achieved by using UAE-HE and UAE-W (36.87 ± 1.09 and 23.03 ± 0.26 mg.g−1 extract dw, respectively). Bis-HHDP-glucose isomers, chestanin and gallic acid were among the most abundant compounds. Bur extracts (MAC-HE and UAE-HE) generally presented the highest antioxidant capacity as measured by TBARS, while the best results in DPPH and reducing power assays were found for shell extracts (MAE-W and MAC-HE). Promising antibacterial activity was noticed for the aqueous extracts of burs, leaves and hydroethanolic extracts of shells, with emphasis on the MAE-W extract of burs that showed bactericidal activity against E. cloacae, P. aeruginosa and S. aureus (MBC 5 mg.mL−1). Overall, it can be concluded that chestnut by-products, including burs, shells and leaves, are sources of polyphenolic compounds with significant antioxidant and antimicrobial activities. The choice of extraction method and solvent greatly influenced the composition and bioactivity of the extracts. These findings highlight the potential of chestnut by-products for the development of natural additives, particularly for food preservation, while also emphasizing the importance of sustainable utilization of agricultural waste materials. Further research is warranted to optimize extraction techniques and explore additional applications for these valuable bioactive compounds.