  Protostellar (class 0/I) disks, having masses comparable to those of their
nascent host stars, and fed continuously from their natal infalling envelopes,
are prone to gravitational instability (GI). Motivated by advances in
near-infrared (NIR) adaptive optics imaging and mm-wave interferometry, we
explore the observational signatures of GI in disks, using hydrodynamical and
Monte Carlo radiative transfer simulations to synthesize NIR scattered light
images and mm dust continuum maps. Spiral arms induced by GI, located at disk
radii of hundreds of AUs, are local overdensities and have their photospheres
displaced to higher altitudes above the disk midplane, arms therefore scatter
more NIR light from their central stars than inter-arm regions, and are
detectable at distances up to 1 kpc by Gemini/GPI, VLT/SPHERE, and
Subaru/HiCIAO/SCExAO. By contrast, collapsed clumps formed by disk
fragmentation have such strong local gravitational fields that their scattering
photospheres are at lower altitudes, such fragments appear fainter than their
surroundings in NIR scattered light. Spiral arms and streamers recently imaged
in four FU Ori systems at NIR wavelengths resemble GI-induced structures and
support the interpretation that FUors are gravitationally unstable protostellar
disks. At mm wavelengths, both spirals and clumps appear brighter in thermal
emission than the ambient disk and can be detected by ALMA at distances up to
0.4 kpc with one-hour integration times at ~0.1 arcsec resolution. Collapsed
fragments having masses >=1 MJ can be detected by ALMA within ~10 minutes.
