We will discuss the recent classification results for non-unital simple C*-algebras. It turns out that the case that the positive cone $K_0(A)$ is not zero can be reduced to the unital cases. We will present the case that C*-algebras are stably projectionless. In particular, we will present the so-called existence theorem for stably projectionless simple C*-algebras, i.e. how to construct maps from one stably projectionless simple C*-algebras to another according to the given data on Elliott invariant.