I have a bit of unusual situation. I own a duplex that is pretty darn old. The basement on it was an afterthought - so the foundation DOES NOT sit on it. Actually, part of the basement was indeed there from before and was used to feed a coal burning stove (??). But later other half was dug out (presumably).

The crux of the problem is that on one side, the brick wall fell down. I believe this brick wall was just a retaining wall for the soil behind it. Now I am tasked to put up a wall again. I do not see any erosion or anything like that, but sure looks ugly. Now I am thinking if I should build a brick wall or build a more solid retaining wall - perhaps with pre-formed concrete block. I googled and binged and all I could find is retaining walls for outside. Any tips on how to go about this?

How you build a retaining wall depends, in part, on how tall it is. How tall is it?

I would say no more than 4 ft.

Form it up with rebar and pour a wall.  I did the concrete block to replace the original bricks once before.  It started cracking again just a few years later. 

+1 on what Leo said.  Also, dependent on how close it is to the house foundation, you may need to compact the dirt after the retaining wall is built.  At a minimum, throw the dirt back behind the retaining wall.

Forming it with rebar and pouring concrete is definitely going to be strong, but that sounds a bit more complicated and time consuming. The brick wall lasted for at least 20 - 30 years. I would say concrete blocks should last longer. Again, this is inside the basement and I will be building some water relief. My plan is to level out the earth behind the wall and build the wall a few inches away from the soil. Then pour wall gravel in between the wall and the soil and compact it.

Forming it with rebar and pouring concrete is definitely going to be strong, but that sounds a bit more complicated and time consuming. The brick wall lasted for at least 20 - 30 years. I would say concrete blocks should last longer. Again, this is inside the basement and I will be building some water relief. My plan is to level out the earth behind the wall and build the wall a few inches away from the soil. Then pour wall gravel in between the wall and the soil and compact it.

perf pipe with soil sock along bottom of wall for drainage