As process nodes continue to shrink, the semiconductor industry faces severe manufacturing challenges. Two most expected technologies may push the limits of next-generation lithography: extreme ultraviolet lithography (EUVL) and electron beam lithography (EBL). EUVL works by emitting intense beams of ultraviolet light that are reflected from a reflective mask into a resist for nanofabrication, while EBL scans focused beams of electrons to directly draw high-resolution feature patterns on a resist without employing any mask. Each of the two technologies encounters unique design challenges and requires solutions for a breakthrough. In this paper, we focus on the design-for-manufacturability issues for EUVL and EBL. We investigate the most critical design challenges of the two technologies, flare and shadowing effects for EUVL, and heating, stitching, fogging, and proximity effects for EBL. Preliminary solutions for these effects are explored, which can contribute to the continuing scaling of the CMOS technology. Finally, we provide future research directions for these key effects.