MOTIVATION: Despite the widespread occurrence of polyploids across the Tree of Life, especially in the plant kingdom, very few computational methods have been developed to handle the specific complexities introduced by polyploids in phylogeny estimation. Furthermore, methods that are designed to account for polyploidy often disregard incomplete lineage sorting (ILS), a major source of heterogeneous gene histories, or are computationally very demanding. Therefore, there is a great need for efficient and robust methods to accurately reconstruct polyploid phylogenies. RESULTS: We introduce Polyphest (POLYploid PHylogeny ESTimation), a new method for efficiently and accurately inferring species phylogenies in the presence of both polyploidy and ILS. Polyphest bypasses the need for extensive network space searches by first generating a multilabeled tree based on gene trees, which is then converted into a (uniquely labeled) species phylogeny. We compare the performance of Polyphest to that of two polyploid phylogeny estimation methods, one of which does not account for ILS, namely PADRE, and another that accounts for ILS, namely MPAllopp. Polyphest is more accurate than PADRE and achieves comparable accuracy to MPAllopp, while being significantly faster. We also demonstrate the application of Polyphest to empirical data from the hexaploid bread wheat and confirm the allopolyploid origin of bread wheat along with the closest relatives for each of its subgenomes. AVAILABILITY AND IMPLEMENTATION: Polyphest is available at https://github.com/NakhlehLab/Polyphest.