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We give a brief overview of the string landscape and techniques used toconstruct string compactifications. We then explain how this motivates thenotion of the swampland and review a number of conjectures that attempt tocharacterize theories in the swampland. We also compare holography in thecontext of superstrings with the similar, but much simpler case of topologicalstring theory. For topological strings, there is a direct definition oftopological gravity based on a sum over a "quantum gravitational foam." In thiscontext, holography is the statement of an identification between a gravity andgauge theory, both of which are defined independently of one another. Thispoints to a missing corner in string dualities which suggests the search for adirect definition of quantum theory of gravity rather than relying on itsstrongly coupled holographic dual as an adequate substitute (Based on TASI 2017lectures given by C. Vafa).

The String Landscape, the Swampland, and the Missing Corner