Context. A significant fraction of all γ-ray sources detected by the Large Area Telescope aboard the Fermi satellite is still lacking a low-energy counterpart. In addition, there is still a large population of γ-ray sources with associated low-energy counterparts that lack firm classifications. In the last 10 years we have undertaken an optical spectroscopic campaign to address the problem of unassociated or unidentified γ-ray sources (UGSs), mainly devoted to observing blazars and blazar candidates because they are the largest population of γ-ray sources associated to date. Aims. Here we describe the overall impact of our optical spectroscopic campaign on sources associated in Fermi-LAT catalogs, coupled with objects found in the literature. In the literature search we kept track of efforts by different teams that presented optical spectra of counterparts or potential counterparts of Fermi-LAT catalog sources. Our summary includes an analysis of additional 30 newly collected optical spectra of counterparts or potential counterparts of Fermi-LAT sources of a previously unknown nature. Methods. New spectra were acquired at the Blanco 4 m and OAN-SPM 2.1 m telescopes, and those available in the Sloan Digital Sky Survey (data release 15) archive. Results. All new sources with optical spectra analyzed here are classified as blazars. Thanks to our campaign, altogether we discovered and classified 394 targets with an additional 123 objects collected from a literature search. We began our optical spectroscopic campaign between the release of the second and third Fermi-LAT source catalogs (2FGL and 3FGL, respectively), classified about 25% of the sources that had uncertain nature and discovered a blazar-like potential counterpart for ∼10% of UGSs listed therein. In the 4FGL catalog, about 350 Fermi-LAT sources have been classified to date thanks to our campaign. Conclusions. The most elusive class of blazars are found to be BL Lacs since the largest fraction of Fermi-LAT sources targeted in our observations showed a featureless optical spectrum. The same conclusion applied to the literature spectra. Finally, we confirm the high reliability of mid-IR color-based methods to select blazar-like candidate counterparts of unassociated or unidentified γ-ray sources.