In the paper we discuss recent observations of the three-dimensional plasma crystals created onboard the International Space Station under microgravity conditions. By using the special scanning technique and the image analysis we could retrieve 3D particle positions. We apply the bond-order parameter method to identify the different lattice types of the plasma crystals. It has been shown that observed plasma crystals contain numerous hcp and fcc clusters. Evidence of a small amount of bcc clusters is also reported. Molecular dynamics simulations of crystallization of a simple Yukawa system reproduce remarkably well all peculiarities of the local properties of observed plasma crystals.