Current brain white matter fiber tracking techniques show a number of problems, including: generating large proportions of streamlines that do not accurately describe the underlying anatomy; extracting streamlines that are not supported by the underlying diffusion signal; and under-representing some fiber populations, among others. In this paper, we describe a novel autoencoder-based learning method to filter streamlines from diffusion MRI tractography, and hence, to obtain more reliable tractograms. Our method, dubbed FINTA (Filtering in Tractography using Autoencoders) uses raw, unlabeled tractograms to train the autoencoder, and to learn a robust representation of brain streamlines. Such an embedding is then used to filter undesired streamline samples using a nearest neighbor algorithm. Our experiments on both synthetic and in vivo human brain diffusion MRI tractography data obtain accuracy scores exceeding the 90% threshold on the test set. Results reveal that FINTA has a superior filtering performance compared to conventional, anatomy-based methods, and the RecoBundles state-of-the-art method. Additionally, we demonstrate that FINTA can be applied to partial tractograms without requiring changes to the framework. We also show that the proposed method generalizes well across different tracking methods and datasets, and shortens significantly the computation time for large (>1 M streamlines) tractograms. Together, this work brings forward a new deep learning framework in tractography based on autoencoders, which offers a flexible and powerful method for white matter filtering and bundling that could enhance tractometry and connectivity analyses.