We introduce wavelet phase harmonics (WPH) statistics: interpretable low-dimensional statistics that describe 2D non-Gaussian fields. These statistics are built from WPH moments, which were recently introduced in the data science and machine learning community. We apply WPH statistics to projected 2D matter density fields from the Quijote N-body simulations of the large-scale structure of the Universe. By computing Fisher information matrices, we find that the WPH statistics place more stringent constraints on four of five cosmological parameters when compared to statistics based on the combination of the power spectrum and bispectrum. We also use the WPH statistics with a maximum entropy model to statistically generate new 2D density fields that accurately reproduce the probability density function, the mean and standard deviation of the power spectrum, the bispectrum, and Minkowski functionals of the input density fields. Although other methods are efficient for either parameter estimates or statistical syntheses of the large-scale structure, WPH statistics are the first statistics that achieve state-of-the-art results for both tasks as well as being interpretable.