Today laser pulses with electric fields comparable to or higher than the electrostatic forces binding valence electrons in atoms and molecules have become a routine tool with applications in laser acceleration of electrons and ions, generation of short wavelength emission from plasmas and clusters, laser fusion, etc. Intense fields are also naturally created during laser filamentation in the air or due to local field enhancements in the vicinity of metal nanoparticles. One would expect that very intense fields would always lead to fast ionization of atoms or molecules. However, recently observed acceleration of neutral atoms [Eichmann et al. (2009) Nature 461:1261-1264] at the rate of 10(15) m/s(2) when exposed to very intense IR laser pulses demonstrated that substantial fraction of atoms remained stable during the pulse. Here we show that the electronic structure of these stable "laser-dressed" atoms can be directly imaged by photoelectron spectroscopy. Our findings open the way to visualizing and controlling bound electron dynamics in strong laser fields and reexamining its role in various strong-field processes, including microscopic description of high order Kerr nonlinearities and their role in laser filamentation [Béjot et al. (2010) Phys Rev Lett 104:103903].