  For a connected graph $G$ and $\alpha\in [0,1)$, the distance
$\alpha$-spectral radius of $G$ is the spectral radius of the matrix
$D_{\alpha}(G)$ defined as $D_{\alpha}(G)=\alpha T(G)+(1-\alpha)D(G)$, where
$T(G)$ is a diagonal matrix of vertex transmissions of $G$ and $D(G)$ is the
distance matrix of $G$. We give bounds for the distance $\alpha$-spectral
radius, especially for graphs that are not transmission regular, propose some
graft transformations that decrease or increase the distance $\alpha$-spectral
radius, and determine the unique graphs with minimum and maximum distance
$\alpha$-spectral radius among some classes of graphs.
