We have developed the first comprehensive simulator for polyploid genomes (PolySim), and demonstrated its value by performing large-scale simulations to examine the effect of different population parameters on the evolution of polyploids. PolySim is unlimited in terms of ploidy, population size, or number of simulated loci. Our process considered the evolution of polyploids from diploid ancestors, polysomic inheritance, inbreeding, recombination rate change in polyploids and gene flow from lower to higher ploidies. We compared the number of segregating SNPs, minor allele frequency, heterozygosity, R2 and average kinship relatedness between different simulated scenarios, and to real data from polyploid species. As expected, allotetraploid populations showed no difference from their ancestral diploids when population size remained constant and there was no gene flow or multivalent pairing between subgenomes. Autotetraploid populations showed significant differences from their ancestors for most parameters and diverged from their ancestral populations faster than allotetraploids. Autotetraploids can have significantly higher heterozygosity, relatedness and extended linkage disequilibrium compared with allotetraploids. Interestingly, autotetraploids were more sensitive to increasing selfing rate and decreasing population size. Multivalent formation can homogenise allotetraploid subgenomes, but this homogenisation requires a higher multivalent rate than previously proposed. Our results can be considered as the first building block to understand polyploid population evolutionary dynamics. PolySim can be used to simulate a wide variety of polyploid organisms that mimic empirical populations which, in combination with quantitative genetics tools, can be used to investigate the power of genome-wide association, genomic selection, or breeding program designs in these species. This article is protected by copyright. All rights reserved.