Glaucoma is an insidious group of eye diseases causing degeneration of the optic nerve, progressive loss of vision, and irreversible blindness. The number of people affected by glaucoma is estimated at 80 million in 2021, with 3.5% prevalence in people aged 40–80. The main biomarker and risk factor for the onset and progression of glaucoma is the elevation of intraocular pressure. However, when glaucoma is diagnosed, the level of retinal ganglion cell death usually amounts to 30–40%; hence, the urgent need for its early diagnosis. Molecular biomarkers of glaucoma, from proteins to metabolites, may be helpful as indicators of pathogenic processes observed during the disease’s onset. The discovery of human glaucoma biomarkers is hampered by major limitations, including whether medications are influencing the expression of molecules in bodily fluids, or whether tests to validate glaucoma biomarker candidates should include human subjects with different types and stages of the disease, as well as patients with other ocular and neurodegenerative diseases. Moreover, the proper selection of the biofluid or tissue, as well as the analytical platform, should be mandatory. In this review, we have summarized current knowledge concerning proteomics- and metabolomics-based glaucoma biomarkers, with specificity to human eye tissue and fluid, as well the analytical approach and the main results obtained. The complex data published to date, which include at least 458 different molecules altered in human glaucoma, merit a new, integrative approach allowing for future diagnostic tests based on the absolute quantification of local and/or systemic biomarkers of glaucoma.