The prevalence of overweight and obesity has progressively increased in the last few years, becoming a real threat to healthcare systems. To date, the clinical management of body weight gain is an unmet medical need, as there are few approved anti-obesity drugs and most require an extensive monitoring and vigilance due to risk of adverse effects and poor patient adherence/persistence. Growing evidence has shown that the gasotransmitter hydrogen sulfide (HS) and, therefore, HS-donors could have a central role in the prevention and treatment of overweight/obesity. The main natural sources of HS-donors are plants from the Alliaceae (garlic and onion), Brassicaceae (e.g., broccoli, cabbage, and wasabi), and Moringaceae botanical families. In particular, polysulfides and isothiocyanates, which slowly release HS, derive from the hydrolysis of alliin from Alliaceae and glucosinolates from Brassicaceae/Moringaceae, respectively. In this review, we describe the emerging role of endogenous HS in regulating adipose tissue function and the potential efficacy of natural HS-donors in animal models of overweight/obesity, with a final focus on the preliminary results from clinical trials. We conclude that organosulfur-containing plants and their extracts could be used before or in combination with conventional anti-obesity agents to improve treatment efficacy and reduce inflammation in obesogenic conditions. However, further high-quality studies are needed to firmly establish their clinical efficacy.