The　concept　of　Hilbert-Schmidt　frame　(HS-frame)　was　first　introduced　by　Sadeghi　and　Arefijamaal　in　2012.　It　is　more　general　than　g-frames,　and　thus,　covers　many　generalizations　of　frames.　This　paper　addresses　the　theory　of　HS-frames.　We　present　a　parametric　and　algebraic　formula　for　all　duals　of　an　arbitrarily　given　HS-frame;　prove　that　the　canonical　HS-dual　induces　a　minimal-norm　expression　of　the　elements　in　Hilbert　spaces;　characterize　when　an　HS-frame　is　an　HS-　Riesz　basis,　and　when　an　HS-Bessel　sequence　is　an　HS-Riesz　sequence　(HS-Riesz　basis)　in　terms　of　Gram　matrices.