The article introduces GenomeScope 2.0 and Smudgeplot, two tools for reference-free profiling of polyploid genomes. GenomeScope 2.0 applies combinatorial theory to model k-mer frequencies in heterozygous and polyploid genomes, using a mixture of negative binomial distributions. It accurately infers genome characteristics such as size, heterozygosity, and repetitiveness from unassembled sequencing data. Smudgeplot is a visualization technique that estimates ploidy and genome structure by analyzing heterozygous k-mer pairs. The tools are evaluated on simulated and real datasets, demonstrating their ability to handle high heterozygosity and complex genomes. The methods are particularly useful for non-model organisms with high ploidy levels, which are underrepresented in genomics studies. The authors apply GenomeScope 2.0 and Smudgeplot to various polyploid species, including *Meloidogyne* and *Fragaria × ananassa*, showing their effectiveness in inferring genome properties and distinguishing between allopolyploid and autopolyploid species.The article introduces GenomeScope 2.0 and Smudgeplot, two tools for reference-free profiling of polyploid genomes. GenomeScope 2.0 applies combinatorial theory to model k-mer frequencies in heterozygous and polyploid genomes, using a mixture of negative binomial distributions. It accurately infers genome characteristics such as size, heterozygosity, and repetitiveness from unassembled sequencing data. Smudgeplot is a visualization technique that estimates ploidy and genome structure by analyzing heterozygous k-mer pairs. The tools are evaluated on simulated and real datasets, demonstrating their ability to handle high heterozygosity and complex genomes. The methods are particularly useful for non-model organisms with high ploidy levels, which are underrepresented in genomics studies. The authors apply GenomeScope 2.0 and Smudgeplot to various polyploid species, including *Meloidogyne* and *Fragaria × ananassa*, showing their effectiveness in inferring genome properties and distinguishing between allopolyploid and autopolyploid species.