Fabrication of multiscale, multi-material three-dimensional (3D) structures at high resolution is difficult using current technologies. This is especially significant when working with hydrated and mechanically weak hydrogel materials. In this work, a new hybrid laser printing (HLP) technology is reported to print complex, multiscale, multimaterial, 3D hydrogel structures with microscale resolution. This technique of fabrication utilizes sequential additive and subtractive modes of material fabrication, that are typically considered as mutually exclusive due to differences in their material processing conditions. Further, compared to current laser writing systems that enforce stringent processing depth limits, HLP is shown to fabricate structures at any depth inside the material. As a proof-of-principle, a Mayan Pyramid with embedded cube-frame is printed using model synthetic polyethylene glycol diacrylate (PEGDA) hydrogel. Printing of ready-to-use open-well chips with embedded microchannels is also demonstrated using PEGDA and gelatin methacrylate (GelMA) hydrogels for potential applications in biomedical sciences. Next, HLP is used in additive and additive modes to print multiscale 3D structures spanning in size from centimeter to micrometers within minutes, which is followed by printing of 3D, multi-material, multiscale structures using this technology. Overall, this work demonstrates that HLP's fabrication versatility can potentially offer a unique opportunity for a range of applications in optics and photonics, biomedical sciences, microfluidics, soft robotics, etc.