  Sidon spaces have been introduced by Bachoc, Serra and Z\'emor in 2017 as the
$q$-analogue of Sidon sets. The interest on Sidon spaces has increased quickly,
especially after the work of Roth, Raviv and Tamo in 2018, in which they
highlighted the correspondence between Sidon spaces and cyclic subspace codes.
Up to now, the known constructions of Sidon Spaces may be divided in three
families: the ones contained in the sum of two multiplicative cosets of a fixed
subfield of $\mathbb{F}_{q^n}$, the ones contained in the sum of more than two
multiplicative cosets of a fixed subfield of $\mathbb{F}_{q^n}$ and finally the
ones obtained as the kernel of subspace polynomials. In this paper we will
mainly focus on the first class of examples, for which we provide
characterization results and we will show some new examples, arising also from
some well-known combinatorial objects. Moreover, we will give a quite natural
definition of equivalence among Sidon spaces, which relies on the notion of
equivalence of cyclic subspace codes and we will discuss about the equivalence
of the known examples.
