They've really helped in the area of modeling the problems. Depending on where you put the unknown, there are several ways to ask the same arithmetic question, eg:
_ + 2 = 5
3 + 2 = _
3 + _ = 5
Overall I think they're a pretty powerful tool, but they require some creativity to really get the most value from them, and they definitely require the use of other learning aids in conjunction like number lines, 99-charts, and base-ten blocks. We also use money, marbles, and other things to try to avoid getting too dependent on a particular manipulative.
Actually the biggest breakthrough we had was making up a card game to learn complements of ten. If you've played "set" you know the basic idea - we lay down 12 cards numbered 0-10, and we compete to see who can make pairs or triples that sum to ten the fastest. She loves it, and she's gotten to where I really have to work to keep up.
Do you have the track? It can help with the concrete/abstract correlation.
You could try clearly printing the numbers on the rods - connecting the abstract symbol to the physical unit of measure. No science behind this, just the gut feeling of a father of 3.
The smallest one is a cube, then a red rod exactly two cubes.
I loved the cuisinaire rods I had as a child, the colours were harmonious and I can still count in that spectrum.
None of my other blocks made patterns as well, they were just innacurate and at a certain age I loved patterns & ziggurats.
They were my absolute favourite building blocks and perhaps helped me become numerate, I certainly knew how many red blocks matched a green and understood add, multiply, & divide operations with coloured blocks intuitively before I knew number symbols.
I think the only change I would try is to add the base 10 number symbols to each one which might make the transition to symbols easier ( maybe put binary notation on the other side* ;)
*[ my dad was a programmer so I learned binary, octal and hex counting as well as base 10 ]
I didn't have the numbered track that seems really cool but there was a very long one in my box, longer than 36 units, maybe it was 100, can't remember, was less fun than the coloured ones.
That the numbers on the track are not coloured according to the blocks seems odd, it is not quite as pretty as the blocks. Perhaps putting symbols on the blocks would make them less appealing to the infant mind ?
I don't recall when or in what depth, but I definitely recall them being involved in my education when I was learning addition and maybe even multiplication.
Like to see some evidence they work and to know why they have gone out of fashion.
 Reading the conclusion in one thesis, their findings were the colors did more harm than good. But the concept of using blocks might have befit.
I used to think it didn't have very much impact. But in retrospect, I think it really opened my young mind to math as spatial reasoning. It wasn't long before I could visualize the answer, or at least a very close approximation, to complex algebra much more quickly than I could do actual calculations.
Oddly enough dominoes somehow lodged themselves in my mind though, I still picture the number ten as two sets of five dots arranged.
If you wanted to use them to teach continuous variables, it would be easy to do so by analogy using the volume of the numbers.
Lego has a different unit height than unit width.
Cuisinaire were better for flat math rather than cubic math ziggurats that I dimly recall building.
replace "Cuisinaire were..." with "Lego were better for flat math rather than the cubic math ziggurats..."
Large Cuisinaire would be good, one could start younger like Duplo but cuisinaire - it seems to me there is a lot of value playing with cuisinaire at a younger age, before any numbers are introduced.