The classical Brunn-Minkowski theory studies the geometry of convex bodies in Euclidean space by use of the Minkowski sum. It originated from H. Brunn's thesis in 1887 and H. Minkowski's paper in 1903. Since there is no universally acknowledged definition of the sum of two sets in hyperbolic space, there has been no Brunn-Minkowski theory in hyperbolic space since 1903. In this talk, for any $p>0$ we introduce a sum of two sets in hyperbolic space, and we call it the hyperbolic $p$-sum. Then we develop a Brunn-Minkowski theory in hyperbolic space by use of our hyperbolic $p$-sum, and we call it the horospherical $p$-Brunn-Minkowski theory. This is joint work with Botong Xu.