High-resolution observations of debris disks by ALMA and direct imaging frequently reveal complex morphologies such as gaps, spirals, and warps. Most existing dynamical processes for explaining such morphologies focus on the role of massive perturbers such as planets or stellar companions, ignoring the gravitational effects of the disk itself. This assumption may not always be justified, especially in view of observations suggesting that debris disks could contain tens of Earth masses in large planetesimals. Indeed, and as we will discuss in this talk, self-gravity of debris disks can be important for producing some of the observed disk structures. Specifically, we will present results showing that the secular interaction between a single planet and an external, self-gravitating debris disk can lead to the formation of a wide gap within the disk. This mechanism is quite robust when the disk is less massive than the planet. Applications of these results for explaining observations will be discussed at length, focusing on three systems (HD 107146, HD 92945, and HD 206893). We will also discuss the implications of our findings (i) for inferring the presence and properties of yet unseen planets and (ii) for setting constraints on the total mass of gapped debris disks.