  If an ultrarelativistic charged particle channels inside a single crystal
with periodically bent crystallographic planes, it emits hard electromagnetic
radiation of the undulator type. Due to similarity of its physical principles
to the ordinary (magnetic) undulator, such a device is termed as the
crystalline undulator. Recent development of a new Monte Carlo code ChaS made
possible a detailed simulation of particle channeling and radiation emission in
periodically bent crystals. According to recent findings, energy of the
electron beam below 1 GeV is sufficient to observe the undulator effect in a
periodically bent crystal. Even more exciting results were obtained for a
crystalline undulator whose bending period is shorter than the period of the
channeling oscillations and the bending amplitude is smaller than the width of
the planar channel. Such a crystalline undulator is far superior to what was
proposed previously. It allows for a large effective number of undulator
periods. Therefore, it is predicted to emit intense undulator radiation in the
forward direction. A narrow undulator peak is seen for both positron and
electron beams. Using positrons is, however, more desirable because in this
case the intensity of the undulator radiation is higher while the background is
lower.
