Motion problems and pixel problems are the two complaints people search for most, so start there. Refresh Rate Test measures what your screen is actually redrawing per second, right now, rather than trusting the spec sheet. Ghosting Test and Frame Skipping Test dig into two specific ways motion can look wrong even when the refresh rate itself checks out — a trailing smear behind moving objects, or frames that silently drop under load.
Dead Pixel Test finds pixels that are stuck black or stuck on one color; Stuck Pixel Fixer is a real, if not guaranteed, attempt at reviving one. Backlight Bleed Test and Screen Uniformity Test look at the panel as a whole in the dark and in flat gray, catching light leaking from the edges or uneven clouding across the surface.
For color and detail, Gradient Test checks for banding in smooth color transitions, and HDR Test shows what your panel is really doing with brightness range and shadow or highlight detail once an HDR signal is playing. Aspect Ratio Test rounds things out by checking whether the image itself is being stretched or squeezed out of true proportion. Worth running through all ten within the return window on any new monitor.