We present theoretical models of black hole (BH) populations in young stellar environments, such as starbursts and young star clusters. Using a population synthesis approach, we compute the formation rates and characteristic properties of single and binary BHs for various representative ages and choices of parameters. We find that most of the BHs (typically 80% for an initial 50% binary fraction) are single, but with many originating from primordial binaries (which either merged into a single massive star or were disrupted following a supernova explosion). A smaller but significant fraction (typically 20%) of the BHs remain in binary systems. Main-sequence stars are the most frequent BH companions, but massive BH-BH binaries are the next most numerous group. The most massive BHs found in our simulations reach~ 80 M☉ and are formed through mergers of massive binary components. If formed in a dense star cluster, such a massive stellar BH may become the seed for growth to a more massive (" intermediate-mass") BH. Although we do not include dynamical interactions, our results provide realistic initial conditions for N-body simulations of dense star clusters (eg, globular clusters) including primordial BHs.