Recent quarkonium results from the STAR experiment Quarkonium measurements in heavy-ion collisions provide insight into the mechanisms which cause the quarkonium bound states to dissociate in the Quark-Gluon Plasma (QGP). The $J/\psi$ suppression and $\Upsilon$ sequential melting provide information on the thermodynamic properties of the QGP, in particular the initial medium temperature. Quarkonium studies in $p$+$p$ and $p$+A collisions serve as the necessary baselines for heavy-ion collisions. They also help to understand the quarkonium production mechanism and the cold nuclear matter effects in $p$+$p$ and $p$+A collisions, respectively. In particular, the charged particle multiplicity dependent studies of quarkonium production in $p$+$p$ collisions could provide information on the interplay of hard vs. soft QCD processes during initial stages. This contribution will focus on recent quarkonium studies from the STAR experiment at RHIC. We will present the $J/\psi$ and $\Upsilon$ measurements in $p$+$p$ collisions at $\sqrt{s} = $~200 and 500~GeV including production cross section, $J/\psi$ production in jets and with jet activity, and normalized quarkonium yield as a function of normalized charged particle multiplicity. Nuclear modification factors and elliptic flow of $J/\psi$ and $\Upsilon$ states in various collision systems ($p$+Au, Au+Au and isobar) at $\sqrt{s_{NN}} = $~200~GeV will be also shown. The presented measurements will be compared to different model predictions and physics implications will be discussed.