Low-light performance is decent.
On the standard model with the 1/3" 13MP Sony Exmor IMX214, it has its limits, which seem to be tighter than phones like the Samsung Galaxy S7 and Google Pixel XL, but the wider f/1.8 aperture does help with letting more light in and OIS seems to be robust enough to handle handshakes until around a shutter speed of 1/8.
Photos tend to expose much brighter than they need to, which results in a bit more noise, so dialing it in with the exposure slider is recommended. The standard camera app includes a night mode that's enabled automatically based on conditions and overall, works quite well.
Overall, photos come out reasonably well, although exposure can sometimes land a bit too high, resulting in a bit more noise when left on its own. Photos also tend to have quite a bit of ISO noise but photo quality is overall quite solid, although it does require some user involvement.
The Moto Z performs quite decently in low-light and can even provide some nice shots with some coaxing and a steady hand, although options like the Google Pixel and the S7 may provide better overall performance. The larger 1/2.4" 21MP Sony IMX338 on the Z Force Droid Edition does provide better performance.