  We study the vacuum structure of a class of Lorentz invariant field theories
where the vacuum expectation values are not constant but are (phase) modulated.
The vacua are classified into spatial, temporal, and light-like modulation
types according to the patterns of spontaneous breaking of translational
symmetry. The conditions for having temporal or light-like modulated vacua
imply severe constraints on the models. We utilize the notion of generalized
Nambu-Goldstone modes which appear in the modulated vacua. Finally, we examine
fluctuation modes around these vacua and discuss their dynamics and the absence
of ghosts.
