  This thesis is concerned with studying the properties of gradings on several
examples of cluster algebras, primarily of infinite type.
  We first consider two finite type cases: $B_n$ and $C_n$, completing a
classification by Grabowski for coefficient-free finite type cluster algebras.
  We then consider gradings arising from $3 \times 3$ skew-symmetric matrices.
We show that the mutation-cyclic matrices give rise to gradings in which all
degrees are positive and have only finitely many associated cluster variables
(excepting one particular case). For the mutation-acyclic matrices, we prove
that all occurring degrees have infinitely many variables.
  We provide a sufficient condition for a graded cluster algebra generated by a
quiver to have infinitely many degrees, based on the presence of a subquiver in
its mutation class. We use this to show that the cluster algebras for (quantum)
coordinate rings of matrices and Grassmannians contain cluster variables of all
degrees in $\mathbb{N}$.
  Next we consider the list (given by Felikson, Shapiro & Tumarkin) of
mutation-finite quivers that do not correspond to triangulations of marked
surfaces. We show that $X_7$ gives rise to only two degrees, both with
infinitely many variables, and that $\widetilde{E}_6$, $\widetilde{E}_7$ and
$\widetilde{E}_8$ give rise to infinitely many variables in some degrees.
  Finally, we study gradings arising from marked surfaces (see Fomin, Shapiro &
Thurston). We adapt a definition by Muller to define the space of valuation
functions on such a surface and prove combinatorially that it is isomorphic to
the space of gradings on the associated cluster algebra. We illustrate this
theory by applying it to the annulus with $n+m$ marked points. We show that the
standard grading is of mixed type. We also give an alternative grading in which
all degrees have infinitely many cluster variables.
