Proteins and the complexes they form are central to nearly all cellular processes. Their flexibility, expressed through a continuum of states, provides a window into their biological functions. Cryogenic electron microscopy (cryo-EM) is an ideal tool to study these dynamic states as it captures specimens in noncrystalline conditions and enables high-resolution reconstructions. However, analyzing the heterogeneous distributions of conformations from cryo-EM data is challenging. We present RECOVAR, a method for analyzing these distributions based on principal component analysis (PCA) computed using a REgularized COVARiance estimator. RECOVAR is fast, robust, interpretable, expressive, and competitive with state-of-the-art neural network methods on heterogeneous cryo-EM datasets. The regularized covariance method efficiently computes a large number of high-resolution principal components that can encode rich heterogeneous distributions of conformations and does so robustly thanks to an automatic regularization scheme. The reconstruction method based on adaptive kernel regression resolves conformational states to a higher resolution than all other tested methods on extensive independent benchmarks while remaining highly interpretable. Additionally, we exploit favorable properties of the PCA embedding to estimate the conformational density accurately. This density allows for better interpretability of the latent space by identifying stable states and low free-energy motions. Finally, we present a scheme to navigate the high-dimensional latent space by automatically identifying these low free-energy trajectories. We make the code freely available at https://github.com/ma-gilles/recovar.