It is believed that not all consistent-looking effective field theories can be embedded in a consistent framework of quantum gravity. Such theories cannot arise as low energy limits of string theory and are said to live in the ‘swampland’. In this talk, the speaker will review two types of swampland theories: those with exact global symmetries, and those that violate the Weak Gravity Conjecture (WGC). He will describe phenomenological implications of these swampland conjectures, as well as recent arguments supporting the WGC.