The $\varUpsilon$ states are a clean probe of the properties of quark-gluon plasma, which can be created in heavy-ion collisions. Each of the $\varUpsilon$ states dissociates at a different temperature in the plasma due to Debye-like screening of the quark-antiquark potential by the surrounding color charges. In order to understand the Cold Nuclear Matter effects, the $\varUpsilon$ production has to be studied in small collision systems such as p+Au or d+Au collisions. Measurements of $\varUpsilon$ production cross section in p+p collisions allow one to study the production mechanism, while its dependence on charged particle multiplicity provides information on the interplay of hard and soft QCD processes.

In this contribution, an overview of the measurements of the production of $\varUpsilon$ states done by the STAR experiment is presented. This includes the rapidity spectra and transverse momentum spectra of different states in p+p collisions at $\sqrt{s}=500\:\mathrm{GeV}$. Nuclear modification factors measured in p+Au, d+Au and Au+Au collisions at $\sqrt{s_{NN}}=200\:\mathrm{GeV}$ are also shown.

The $\varUpsilon(1S)$ spectra in p+p collisions are reasonably described by the Color Evaporation Model calculation, while overestimated by calculations based on Non-Relativistic QCD formalism coupled with the Color Glass Condensate effective theory. In Au+Au collisions, the $\varUpsilon(1S)$ is similarly suppressed to what observed at the LHC, while $\varUpsilon(2S+3S)$ are more suppressed than $\varUpsilon(1S)$ in central collisions. This is an indication of sequential suppression of $\varUpsilon$ states at $\sqrt{s_{NN}}=200\:\mathrm{GeV}$. The model calculations are consistent with the data.