The swampland program tries to identify seemingly consistent low energy effective field theories that become inconsistent when coupled to Einstein's gravity. Such low energy effective field theories are said to be in the swampland. Criteria that place low energy effective theories in the swampland come in terms of conjectures for which we have varying degrees of evidence (but usually no proof due to our lack of understanding of non-perturbative quantum gravity). After a longer introduction with several examples, I will review recent swampland conjectures that constrain the existence of dS and AdS solutions in string theory. Then I will discuss potential counterexamples and refinements of these conjectures. While the dS swampland conjectures and their counterexamples are more relevant for our own universe, they are fairly difficult to improve on. However, it seems possible to reach a consensus in the AdS case. While I will focus on the gravity side of such AdS solutions, there are important implications for the AdS/CFT duality as well.