In the last decade, it has become clear that the dust-enshrouded star formation contributes significantly to early galaxy evolution. Detection of dust is therefore essential in determining the properties of galaxies in the high-redshift universe. This requires observations at the (sub-)millimeter wavelengths. Unfortunately, sensitivity and background confusion of single dish observations on the one hand, and mapping efficiency of interferometers on the other hand, pose unique challenges to observers. One promising route to overcome these difficulties is intensity mapping of fluctuations which exploits the confusion-limited regime and measures the collective light emission from all sources, including unresolved faint galaxies. We discuss in this contribution how 2D and 3D intensity mapping can measure the dusty star formation at high redshift, through the Cosmic Infrared Background (2D) and [CII] fine structure transition (3D) anisotropies.