Planetary soft landing is a critical challenge in space exploration, requiring precision and robustness to ensure the safety and success of lander missions. Convex programming, known for its global optimality and computational efficiency, offers significant advantages for designing landing trajectories and control strategies under complex constraints and uncertainties. In this presentation, we explore the application of convex programming to develop algorithms for soft landing on planetary surfaces. We introduce our approaches that utilize first-order methods and distributed optimization to enhance computational speed and scalability. The first-order methods are particularly advantageous as they are simpler and can be efficiently implemented on Graphics Processing Units (GPUs), leveraging their parallel processing capabilities to handle large-scale problems more effectively. Furthermore, we discuss the use of various testbeds, including indoor flight test facilities and rocket test beds, which play a pivotal role in validating our proposed algorithms and ensuring their reliability and effectiveness in real-world scenarios. This talk highlights how cutting-edge optimization techniques, combined with advanced computational resources and rigorous testing, pave the way for safer and more efficient planetary landings.