In recent years, additive manufacturing (AM) technologies have attracted significant interest in many industrial and research fields, particularly in tissue engineering. Printed structures used as physical and bioactive supports for tissue regeneration are becoming increasingly complex so as to mimic natural tissues in order to answer future medical needs. Reproducing the biological environment of a native tissue from the microscopic to the macroscopic scale appears to be the best strategy for effective regeneration. Recent advances in AM have led to the production of scaffolds designed with a high precision. This Review presents results concerning two AM technologies which enable the highest accuracy of scaffold design to be obtained, with a precision down to the nanoscale. The first technique is based on a two-photon polymerization (TPP) process, while the other is based on a direct-writing electrospinning (DWES) system. Here, we present an overview of the fabrication mechanisms, the final scaffold properties, and their applications in tissue engineering. The production of highly resolved structures offers new possibilities for studying cell behavior in a controlled environment and also for adjusting the desired scaffold properties to address current and future needs in tissue engineering. The current technical limitations and future challenges are thus also discussed in this Review.