$R^1$, $R^2$ and $R^3$-continua were defined by S. T. Czuba in 1980, in particular he showed that the existence of any one of these sets in a continuum $X$ implies the noncontractibility of $X$. Also, $R^i$-continua have proved to be useful when studying noncontractibility of hyperspaces. In this talk we recall these concepts and we present some relations between them in continua and hyperspaces.