Short answers, pulled from the story.
The earliest compound microscopes appeared in Europe around 1620 with demonstrations by Cornelis Drebbel in London in 1621 and in Rome in 1624. Dutch spectacle-maker Johannes Zachariassen claimed his father Zacharias Janssen invented the device as early as 1590, though this claim is considered unlikely due to birth date discrepancies.
August Köhler developed Köhler illumination in August 1893 to provide extremely even lighting that overcomes limitations of older sample illumination techniques. This method ensures the image of the light source is not visible within the sample image.
Dutch physicist Frits Zernike received the Nobel Prize in physics in 1953 for developing phase contrast illumination. This technique allows imaging of transparent samples like live mammalian cells without using staining techniques.
The maximum resolving power of optical microscopes is typically limited to around 200 nanometers because of the diffraction limit of visible light. Conventional lenses cannot resolve separate points below approximately 200 nm even with high magnification.
The Nobel Prize in Chemistry was awarded on the 8th of October 2014 to Eric Betzig, William Moerner and Stefan Hell for their work on super-resolved fluorescence microscopy. Stefan Hell also received the 10th German Future Prize in 2006 for his STED microscope methodologies.