Ripening of fleshy fruits involves complex physiological, biochemical, and molecular processes that coincide with various changes of the fruit, including texture, color, flavor, and aroma. The processes of ripening are controlled by ethylene in climacteric fruits and abscisic acid (ABA) in non-climacteric fruits. Increasing evidence is also uncovering an essential role for polyamines (PAs) in fruit ripening, especially in climacteric fruits. However, until recently breakthroughs have been made in understanding PA roles in the ripening of non-climacteric fruits. In this review, we compare the mechanisms underlying PA biosynthesis, metabolism, and action during ripening in climacteric and non-climacteric fruits at the physiological and molecular levels. The PA putrescine (Put) has a role opposite to that of spermidine/spermine (Spd/Spm) in cellular metabolism. Arginine decarboxylase (ADC) is crucial to Put biosynthesis in both climacteric and non-climacteric fruits. S-adenosylmethionine decarboxylase (SAMDC) catalyzes the conversion of Put to Spd/Spm, which marks a metabolic transition that is concomitant with the onset of fruit ripening, induced by Spd in climacteric fruits and by Spm in non-climacteric fruits. Once PA catabolism is activated by polyamine oxidase (PAO), fruit ripening and senescence are facilitated by the coordination of mechanisms that involve PAs, hydrogen peroxide (H2O2), ABA, ethylene, nitric oxide (NO), and calcium ions (Ca2+). Notably, a signal derived from PAO5-mediated PA metabolism has recently been identified in strawberry, a model system for non-climacteric fruits, providing a deeper understanding of the regulatory roles played by PAs in fleshy fruit ripening.