The invention is directed to methods for synthesizing oligonucleotides directly on biomolecules or cells living or fixed. In some embodiments, template-free enzymatic synthesis is implemented under biological conditions with successive cycles of (i) enzymatic addition of a 3′-O-blocked nucleoside triphosphate and (ii) enzymatic deblocking of the incorporated nucleotide to regenerate a free 3′ hydroxyl. The invention has applications in single-cell cDNA library construction and analysis.