Despite the foundational role of Indo-European studies in historical-comparative linguistics, there are many persistent problems in the reconstruction of IE stops. Unresolved issues include: (1) the number of velar series to be posited for Proto-Indo-European; (2) unexplained variation between voiced non-aspirates and voiced aspirates; (3) irregular correspondences involving /d/ and /l/; (4) the typological naturalness of the reconstructed stop system. A three-way velar distinction is required for PIE, at least in some phonological environments. Albanian maintains the three-way distinction, while satem languages provide evidence for morphophonemic alternation among three series. However, pre-IE likely had only a two-way distinction, with subphonemic variation between palatalized and non-palatalized allophones of plain velars. This distinction became phonemic by secondary split at the PIE stage. Many hitherto unexplained examples of variation between *g/*g/*d vs. *gh/*gh/*dh, respectively, result from regular change of voiced non-aspirates plus the a-coloring laryngeal to voiced aspirates. This early change, which probably happened independently in Sanskrit, Greek, and Germanic, is in accord with the reconstruction of the a-coloring laryngeal as a voiceless fricative. However, not all problematic examples of voiced aspirate vs. voiced non-aspirate can be accounted for by this hypothesis. Some are due to a sporadic process of post-nasal deaspiration in pre-Greek, while others remain unexplained. Irregular correspondences involving /d/ and /l/ provide evidence for the reconstruction of a rare PIE cluster *dl. This cluster was phonotactically disfavored and was therefore subject to sporadic modification throughout the IE language family. The traditional reconstructed stop system of PIE has been criticized as being unnatural in synchronic typological terms. The so-called glottalic reconstruction is more typologically natural. However, the glottalic system is not well-suited to account for the historical developments from PIE to its attested daughter languages. For PIE, the traditional reconstruction is to be preferred on the basis of historical and comparative evidence, although the pre-IE system may have been glottalic.