Abstract: I will review our series of successful programs to dissect the interstellar medium of distant, star-forming galaxies with the Atacama Large Millimeter Array (ALMA). In particular, I will discuss surveys of the set of HI-selected galaxies known as the damped Lya systems (DLAs). We resolve, in part, a decades old struggle to identify the galactic counterparts of these DLAs and thereby place them firmly in the modern picture of galaxy formation. I will also highlight high spectral and spatial resolution observations of the Wolfe Disk, a z~4 galaxy with a Milky Way-like rotation curve.