Polyploids - organisms that have multiple sets of chromosomes - are common in certain plant and animal taxa, and can be surprisingly stable. The evidence that has emerged from genome analyses also indicates that many other eukaryotic genomes have a polyploid ancestry, suggesting that both humans and most other eukaryotes have either benefited from or endured polyploidy. Studies of polyploids soon after their formation have revealed genetic and epigenetic interactions between redundant genes. These interactions can be related to the phenotypes and evolutionary fates of polyploids. Here, I consider the advantages and challenges of polyploidy, and its evolutionary potential.