  The recent realization of synthetic spin-orbit coupling represents an
outstanding achievement in the physics of ultracold quantum gases. In this
review we explore the properties of a spin-orbit-coupled Bose-Einstein
condensate with equal Rashba and Dresselhaus strengths. This system presents a
rich phase diagram, which exhibits a tricritical point separating a
zero-momentum phase, a spin-polarized plane-wave phase, and a stripe phase. In
the stripe phase translational invariance is spontaneously broken, in analogy
with supersolids. Spin-orbit coupling also strongly affects the dynamics of the
system. In particular, the excitation spectrum exhibits intriguing features,
including the suppression of the sound velocity, the emergence of a roton
minimum in the plane-wave phase, and the appearance of a double gapless band
structure in the stripe phase. Finally, we discuss a combined procedure to make
the stripes visible and stable, thus allowing for a direct experimental
detection.
