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We present the results from the HST WFC3 and ACS data on an archetypal galaxy undergoing ram pressure stripping (RPS), ESO 137-001, in the nearby cluster Abell 3627. ESO 137-001 is known to host a prominent stripped tail detected in many bands from X-rays, H α to CO. The HST data reveal significant features indicative of RPS such as asymmetric dust distribution and surface brightness as well as many blue young star complexes in the tail. We study the correlation between the blue young star complexes from HST, H ii regions from H α (MUSE), and dense molecular clouds from CO (ALMA). The correlation between the HST blue star clusters and the H ii regions is very good, while their correlation with the dense CO clumps are typically not good, presumably due in part to evolutionary effects. In comparison to the starburst99 + cloudy model, many blue regions are found to be young (<10 Myr) and the total star formation (SF) rate in the tail is 0.3–0.6 M⊙ yr−1 for sources measured with ages less than 100 Myr, about 40 per cent of the SF rate in the galaxy. We trace SF over at least 100 Myr and give a full picture of the recent SF history in the tail. We also demonstrate the importance of including nebular emissions and a nebular to stellar extinction correction factor when comparing the model to the broad-band data. Our work on ESO 137-001 demonstrates the importance of HST data for constraining the SF history in stripped tails.