The impact of plastics on the environment can be mitigated by employing biobased and/or biodegradable materials (i.e., bioplastics) instead of the traditional “commodities”. In this context, poly (butylene succinate) (PBS) emerges as one of the most promising alternatives due to its good mechanical, thermal, and barrier properties, making it suitable for use in a wide range of applications. Still, the PBS has some drawbacks, such as its high crystallinity, which must be overcome to position it as a real and viable alternative to “commodities”. This contribution covers the actual state-of-the-art of the PBS through different sections. The first section reviews the different synthesis routes, providing a complete picture regarding the obtained molecular weights and the greener alternatives. Afterward, we examine how different strategies such as random copolymerization and the incorporation of fillers can effectively modulate PBS properties to satisfy the needs for different applications. The impact of these strategies is evaluated in the crystallization behavior, crystallinity, mechanical and barrier properties, and biodegradation. The biodegradation is carefully analyzed, highlighting the wide variety of methodologies existing in the literature to measure PBS degradation through different routes (hydrolytic, enzymatic, and soil).