The question comes up here often enough that I thought it might be of help to have a photographic record of the various sights that came (some factory and some after-market) for the Remington Model 37 Rangemaster rifles. The last of these rifles came off the line in 1954 or 1955, after which time it was replaced by the Remington 40x.
The front sight base for the Remington 37 was one peculiar to this rifle alone. Here it is:
The front sight normally supplied was made by Redfield:
This sight was made specially to fit on the base seen above, which has the radius cut on the left side, rather than the more normal location on the right. While the attaching thumb screw is on the right side, it actuates a "hook" on the left side of the sight which engages the radius cut on the special base.
Most early Remington 37 rifles came with a special receiver diopter sight designed by Remington. It fit on one of two dovetail adapters (either long or short.)
Here is the long base:
Here are both the long and short bases. Both came with the Remington 37 originally, giving the shooter a choice as to which suited the shooter better.
Here is the Remington designed receiver sight fitted on the long base. The Remington receiver sight came with a Parker-Hale six hole eyepiece that allowed by the simple turn of a dial various rear aperture sizes. The notches on the top of the long base gave the shooter up to six different locations where one can lock down the rear sight which allowed for a simple yet sturdy way to adjust eye relief. With the short base the shooter had but one choice of sight position.
And here are closer looks at the sight:
Less commonly encountered was this Marble-Goss receiver sight, which was factory fitted on some Model 37 rifles, and retrofitted to others. It was attached to the rifle by means of a special adapter base made by Marbles for that purpose. Note the base is marked "Rem. 37":
Perhaps the rear sight least often encountered was the Wittek-Vaver sight, which arguably was the finest of the sights fitted to the Remington 37. These sights were built like a Swiss watch and are much sought after today:
It should be noted that I have seen catalogs which claim there was a version of the Lyman #52 sight adapted to the Remington 37, but in 40 years of collecting these rifles, I have never seen one. It may exist only on paper. Like unicorns, I will believe in it when I see one.
Beginning in 1951 (per the Stoeger Shooter's Bible) Remington 37 rifles were fitted with the ubiquitous Redfield Olympic sights, both front and rear, the rear sight attached by means of this Redfield base:
Here is the Olympic sight base installed on a Remington 37:
And to show how it all came together, here is a Redfield Olympic receiver sight mounted on a Remington 37:
The Redfield International Match or Redfield Palma sight (both of which came into being after the Remington 37 production run) also fit on the Olympic sight base. While, strictly speaking, the International Match and Palma sights were not factory options for the Remington 37, they can be used on the Olympic base.
When the Olympic front sight was utilized, a more conventional dovetail base was used instead of the front sight base pictured above.
I hope this basic information will be of use to those fortunate enough to own a Remington 37, and to any future Remington 37 owners.
All the best -----
BRP
The front sight base for the Remington 37 was one peculiar to this rifle alone. Here it is:

The front sight normally supplied was made by Redfield:

This sight was made specially to fit on the base seen above, which has the radius cut on the left side, rather than the more normal location on the right. While the attaching thumb screw is on the right side, it actuates a "hook" on the left side of the sight which engages the radius cut on the special base.
Most early Remington 37 rifles came with a special receiver diopter sight designed by Remington. It fit on one of two dovetail adapters (either long or short.)
Here is the long base:


Here are both the long and short bases. Both came with the Remington 37 originally, giving the shooter a choice as to which suited the shooter better.

Here is the Remington designed receiver sight fitted on the long base. The Remington receiver sight came with a Parker-Hale six hole eyepiece that allowed by the simple turn of a dial various rear aperture sizes. The notches on the top of the long base gave the shooter up to six different locations where one can lock down the rear sight which allowed for a simple yet sturdy way to adjust eye relief. With the short base the shooter had but one choice of sight position.

And here are closer looks at the sight:


Less commonly encountered was this Marble-Goss receiver sight, which was factory fitted on some Model 37 rifles, and retrofitted to others. It was attached to the rifle by means of a special adapter base made by Marbles for that purpose. Note the base is marked "Rem. 37":


Perhaps the rear sight least often encountered was the Wittek-Vaver sight, which arguably was the finest of the sights fitted to the Remington 37. These sights were built like a Swiss watch and are much sought after today:

It should be noted that I have seen catalogs which claim there was a version of the Lyman #52 sight adapted to the Remington 37, but in 40 years of collecting these rifles, I have never seen one. It may exist only on paper. Like unicorns, I will believe in it when I see one.
Beginning in 1951 (per the Stoeger Shooter's Bible) Remington 37 rifles were fitted with the ubiquitous Redfield Olympic sights, both front and rear, the rear sight attached by means of this Redfield base:

Here is the Olympic sight base installed on a Remington 37:

And to show how it all came together, here is a Redfield Olympic receiver sight mounted on a Remington 37:

The Redfield International Match or Redfield Palma sight (both of which came into being after the Remington 37 production run) also fit on the Olympic sight base. While, strictly speaking, the International Match and Palma sights were not factory options for the Remington 37, they can be used on the Olympic base.

When the Olympic front sight was utilized, a more conventional dovetail base was used instead of the front sight base pictured above.
I hope this basic information will be of use to those fortunate enough to own a Remington 37, and to any future Remington 37 owners.
All the best -----
BRP