A continuum $X$ has unique cone provided that the following property holds: if $Y$ is a continuum and ${\rm Cone}(X)$ is homeomorphic to ${\rm Cone}(Y)$, then $X$ is homeomorphic to $Y$. In this talk we consider the problem of the uniqueness of cones for some not locally connected continua, e.g. the indecomposable continua and the compactifications of the ray.