In order to photograph at night, you need to set the camera to much higher ISO levels, and that can generate noise. Various photo editing programs and filters can reduce that somewhat, but one way to solve the problem is to work with the noise to create a particular effect. The image below was shot at ISO 16000, a shutter speed of 400, and at aperture f/20. When processing the image, I edited the moon by separating it from the background and worked with sharpening and noise reduction/blur filters in Photoshop to get the effect I liked. I was not concerned with having an absolutely sharp image.
In this image from Lisbon, I was mostly interested in the streetcar and the hotel. This was ISO 1600 and a shutter speed at 100. The people walking show some blur, and the man with his arm outstretched has a blurred and unrecognizable face. The solution is to shoot at much higher ISOs and faster shutter speed and deal with the noise issue as with the moon shot above. Or make blur part of the overall effect.
In the photo below, I was most interested in the interaction between the grandfather and the granddaughter. Her face is not large and all the features are not shown in full detail, but there is enough sharpness to show her smile and line of sight. I dealt with the noise issues as discussed above, but felt this worked because what I wanted to show was sufficiently sharp, in focus, and discernible. This is also a situation where I used selective sharpening over parts of the image and did not crop too tightly. I didn’t care if some of the things were soft focus.