Bioinspired and biomimetic soft machines rely on functions and working principles that have been abstracted from biology but that have evolved over 3.5 billion years. So far, few examples from the huge pool of natural models have been examined and transferred to technical applications. Like living organisms, subsequent generations of soft machines will autonomously respond, sense, and adapt to the environment. Plants as concept generators remain relatively unexplored in biomimetic approaches to robotics and related technologies, despite being able to grow, and continuously adapt in response to environmental stimuli. In this research review, we highlight recent developments in plant-inspired soft machine systems based on movement principles. We focus on inspirations taken from fast active movements in the carnivorous Venus flytrap (Dionaea muscipula) and compare current developments in artificial Venus flytraps with their biological role model. The advantages and disadvantages of current systems are also analyzed and discussed, and a new state-of-the-art autonomous system is derived. Incorporation of the basic structural and functional principles of the Venus flytrap into novel autonomous applications in the field of robotics not only will inspire further plant-inspired biomimetic developments but might also advance contemporary plant-inspired robots, leading to fully autonomous systems utilizing bioinspired working concepts.