There are a few types of microscopy probably being used here, but effectively we can detect color insofar as we are using a light wavelength. The Abbe equation

There are a few types of microscopy probably being used here, but effectively we can detect color insofar as we are using a light wavelength. The Abbe equation describes the maximum resolution (The distance at which two points look like one) of a microscope based on wavelength can have (Around 200-250 nanometers for light), though the 2014 Nobel in Chemistry was awarded to scientists who have developed techniques that cleverly subvert this (Achieving resolution under 100 nanometers). Many of the pictures also use electron microscopy, which can achieve significantly lower resolutions. These images have been post-processed significantly. Something that was shocking to me when I first performed fluorescent microscopy was how much "prettifying" is done on these images. Many fluorescent microscopes output a single brightness value that you interpret to be the color you are looking for, meaning that you could literally color your image however you wanted. This was especially useful because red and green were commonly detected colors, but a lab member was color blind.