  We describe the processing of the PHANGS-ALMA survey and present the
PHANGS-ALMA pipeline, a public software package that processes calibrated
interferometric and total power data into science-ready data products.
PHANGS-ALMA is a large, high-resolution survey of CO J=2-1 emission from nearby
galaxies. The observations combine ALMA's main 12-m array, the 7-m array, and
total power observations and use mosaics of dozens to hundreds of individual
pointings. We describe the processing of the u-v data, imaging and
deconvolution, linear mosaicking, combining interferometer and total power
data, noise estimation, masking, data product creation, and quality assurance.
Our pipeline has a general design and can also be applied to VLA and ALMA
observations of other spectral lines and continuum emission. We highlight our
recipe for deconvolution of complex spectral line observations, which combines
multiscale clean, single scale clean, and automatic mask generation in a way
that appears robust and effective. We also emphasize our two-track approach to
masking and data product creation. We construct one set of "broadly masked"
data products, which have high completeness but significant contamination by
noise, and another set of "strictly masked" data products, which have high
confidence but exclude faint, low signal-to-noise emission. Our quality
assurance tests, supported by simulations, demonstrate that 12-m+7-m
deconvolved data recover a total flux that is significantly closer to the total
power flux than the 7-m deconvolved data alone. In the appendices, we measure
the stability of the ALMA total power calibration in PHANGS--ALMA and test the
performance of popular short-spacing correction algorithms.
