Built-in cabinets in older homes often need to have the hinges replaced. Hinges may be missing or broken, causing doors to close incorrectly, or previous replacements were incorrect. Identifying the type of hinge you have is the first step to finding a correct replacement.
At the turn of the 20th century, family homes did not have built-in cabinetry. Kitchens had open shelving and freestanding cabinets for storage. By the 1920s, homes were being built with built-in cabinets. Most cabinetry featured inset or partial inset doors. Surface mounted hinges were common and often decorative, though butt hinges and half surface hinges were also used.
How much of the hinge you see when the door is closed is a good way to narrow down the type of hinge you have:

Butt Hinge: When the door is closed, only the barrel or knuckles are visible.

Full Surface Hinge: Entire hinge is visible on the frame and door face.

Half Surface Hinge: One half of the hinge is on the door face, the other is on the frame's inside edge.
If your hinges are missing, check for old screw holes and how the door fits in the frame to determine mounting style.
By the mid-century era, cabinets often had partial inset or full overlay doors. The most common hinge was the semi-concealed hinge, visible only on the face of the cabinet when closed.

Semi-Concealed Hinges: When the door is closed, half the hinge is visible on the cabinet face.
Pivot hinges were also common, either mounted above/below or into the edge of the door. Steel cabinets from the 1950s often used manufacturer-specific pivot hinges.
European hinges have become the standard over the past 40 years. These are fully concealed when the door is closed.
To review: Do you see all, part, or none of the hinge? When closed, does the door recess fully, partially, or sit on the outside of the frame?
Finding the Right Hinge
Once you identify your hinge type, you'll need to find the correct size or style. Modern hinges differ from vintage ones, so expect to re-drill screw holes or modify the cabinet. Always replace all hinges on a door to avoid misalignment.
Butt Hinges
Measure when laid open like a book. Height is measured along the barrel, width is the full open span. Watch for mortise depth and hinge thickness.
Full Surface Hinges
Check whether your application is flush or offset. Flush = door is recessed. Offset = door sits proud of the frame. Offset is typically 3/8".
Half Surface Hinges
Half mounts inside the frame, half on the door face. Ensure enough space and good wood for screw placement.
Semi-Concealed Hinges
Check if they screw into wood or use a cutout — the latter are called Demountable Hinges. Reverse bevel doors need Reverse Bevel Hinges. Doors with a stepped edge need Partial Inset Hinges. Flat back doors use Overlay Hinges.

Demountable Hinges: Mount into a cut-out in the door or frame.

Reverse Bevel Hinges: For doors with a beveled back edge.

Partial Inset Hinges: For doors with a stepped edge that recess into the frame.

Overlay Hinges: For doors that overlap the cabinet opening.
Some semi-concealed hinges wrap around the frame edge. For those, you'll need the overlay measurement — how much the door overlaps the cabinet face.
Partial Inset Hinges
Measure both the lip (how much overlaps the frame) and the inset (how much recesses into the frame).

Pivot Hinges
Note mounting style (above/below or side-mounted). Check for brand stamps. Minimal hardware is visible when closed.

Pivot Hinges: Often mostly concealed when the door is closed.
European Hinges
Available for nearly all applications. For a full guide, click HERE.
Note: There are few industry-wide standards for cabinet hinges. Expect variation in screw placement, size, and finish. But with some adjustments, you can usually find a functional fit.