Computer simulations of bulk and vapor deposited amorphous ices are presented. The structure of the bulk low density amorphous ice is in good agreement with experiments on pressure disordered amorphous ice. Both the low density bulk ice and the vapor deposited ices exhibit strong ordering. Vapor deposition of hot (300 K) water molecules onto a cold (77 K) substrate yields less porous ices than deposition of cold (77 K) water molecules onto a cold subtrate. Both vapor deposited ices are more porous than the bulk amorphous ice. The structure of bulk high density amorphous ice is only in fair agreement with experimental results. Attempts to simulate high density amorphous icevia vapor deposition were not successful. Electron diffraction results on vapor deposited amorphous ice indicate that the temperature of the nucleation of the cubic phase depends upon the amount of time between the deposition and the onset of crystallization, suggesting that freshly deposited ice layers reconstruct on times of the order of hours. The temperature dependence of the microporosity of the vapor deposited amorphous ices might affect laboratory experiments that are aimed at simulating astrophysical ices in the context of the origin of prebiotic organic material and its transport to the Earth.