In recent years, significant progress has been made in functional soft materials, alongside advances in nano/micromanufacturing techniques, driving the evolution of soft grippers to the forefront of robotics innovation. Compared to their traditional rigid counterparts, soft grippers offer unparalleled adaptability, effortlessly conforming to objects of varying sizes and shapes. This comprehensive review explores the latest trends shaping the landscape of soft robotic grippers, providing insights into their diverse functionalities and applications. The exploration begins with an examination of the various actuation mechanisms utilized by soft grippers, including cable or tendon-driven, pneumatic, electroactive, and thermoactive systems. Additionally, the review delves into the intricacies of grasping and manipulating mechanisms, spanning from multi-finger configurations to innovative approaches, such as jamming, suction, and adhesion grasping. Notably, hybrid grippers, which integrate multiple actuation and grasping mechanisms, are of particular interest, thereby enhancing the range of functionalities offered by these grippers. Finally, the review briefly addresses current limitations and future directions in the field.