Engineering ultrashort laser pulses is crucial for advancing fundamental research fields and applications. Controlling their spatiotemporal behavior, tailored to specific applications, can unlock new experimental capabilities. However, achieving this control is particularly challenging due to the difficulty in independently structuring their intensity and spatial phase distributions, given their polychromatic bandwidth. This article addresses this challenge by presenting a technique for generating flying structured laser pulses with tunable spatiotemporal behavior. We developed a comprehensive approach to directly design and govern these laser pulses. This method elucidates the role jointly played by the pulse’s spatiotemporal couplings and its prescribed phase gradient in governing the pulse dynamics. It evidences that the often-overlooked design of the phase gradient is indeed essential for achieving programmable spatiotemporal control of the pulses. By tailoring the prescribed phase gradient, we demonstrate the creation of, to our knowledge, novel families of flying structured laser pulses that travel at the speed of light in helical spring and vortex multi-ring forms of different geometries. The achieved control over the dynamics of their intensity peaks and wavefronts is analyzed in detail. For instance, the intensity peak can be configured as a THz rotating light spot or shaped as a curve, enabling simultaneous substrate illumination at rates of tens of THz, far exceeding the MHz rates typically used in laser material processing. Additionally, the independent manipulation of the pulse wavefronts allows local tuning of the orbital angular momentum density carried by the beam. Together, these advancements unveil advantageous capabilities that have been sought after for many years, especially in ultrafast optics and light-matter interaction research.AI Voice