Climate change is a pressing matter of anthropogenic nature to which agriculture contributes by abusing production inputs such as inorganic fertilizers and fertigation water, thus degrading land and water sources. Moreover, as the increase in the demand of food in 2050 is estimated to be 25 to 70% more than what is currently produced today, a sustainable intensification of agriculture is needed. Biostimulant substances are products that the EU states work by promoting growth, resistance to plant abiotic stress, and increasing produce quality, and may be a valid strategy to enhance sustainable agricultural practice. Presented in this review is a comprehensive look at the scientific literature regarding the widely used and EU-sanctioned biostimulant substances categories of silicon, seaweed extracts, protein hydrolysates, and humic substances. Starting from their origin, the modulation of plants’ hormonal networks, physiology, and stress defense systems, their in vivo effects are discussed on some of the most prominent vegetable species of the popular plant groupings of cucurbits, leafy greens, and nightshades. The review concludes by identifying several research areas relevant to biostimulant substances to exploit and enhance the biostimulant action of these substances and signaling molecules in horticulture.