I will try to present the current state of various projects for follow-up observations with ALMA (and NOEMA) of high-z submillimeter galaxies discovered with Herschel (SMGs), both for projects in progress or planned ones. This could include: characterization of prominent, exceptional sources such as strong gravitational lenses, sources with z>4-5, HyLIRGs, etc.; redshift determination from CO lines; nature, structure and properties of the sources, discs or mergers; high-z (proto-)clusters; use of strong lensing for high sensitivity studies of the interstellar medium and of various molecules such as H2O; prospects for studying chemistry, isotopologues, outflows, AGN, etc. I will specially emphasize cases allowing the best synergies between NOEMA and ALMA.