I'm responding off the top of my head, here, but I think what follows is generally correct, even if I may have muddled a few details. It's been a while. I first looked into Roman concrete years ago, after seeing a photo of some Roman harbor works which were a bit eroded, but still an obvious and functional break wall (mole). I thought: "How'd they make that? And why has it lasted so long?" The second question because modern Portland cement roads, curbs and sidewalks start looking pretty raggedy after just a few years, at least in my
experience. This was before the recent flush of renewed interest in Roman concrete, so there was a lot less to go on, back then.
There are actually several variations of Roman concrete, depending on the intended purpose. There are analogs of Roman concrete from other parts of the world, too.
As I recall, Vitruvius discusses some of the recipes in
De Architectura. These all rely on heat activated (i.e. chemically converted) earthen materials. In the case of Roman concrete, either "harena fossica" - "pit sand" - which was a naturally occurring volcanic sand excavated from the slopes of Vesuvius, or "testa" - ground up fired terra cotta; in today's technical parlance this ground terra cotta is called "meta-kaolin", and we distinguish between different grades, depending on the temperature at which it has been fired. For the latest research on the modern versions, "geopolymer" will be a good keyword to use when poking around, in addition to "meta-kaolin". I think there was also a "carbunculus" material (sounds straight out of Harry Potter, I know) mentioned in connection with concrete in Vitruvius, too. (Edit: "pozzolan" or "pozzolana" are vernacular terms for the general
class of heat activated earthen materials, now in the technical vocabulary, and including things as diverse as coal power plant fly
ash or rice hull ash. That is another good search term.)
The Pantheon used volcanic tuff aggregate in the roof dome to yield a lightweight concrete. The tuff is full of gas bubbles, so it made for something more like an aerated concrete.
In the Middle East, similar concretes were known as "serooj" (Romanized spellings vary). Today, this term seems also to be applied to modern Portland cement. From lining cisterns and water conduits in the mountain oases of Oman, to plastering qanats (
underground aqueducts), to waterproofing yakchals (ice houses) near Yazd, Iran, these seroojs have a long history. Firing a stacked pile of hand molded clay disks interlayered with dried manure pats, then collecting the fired clay and ashes when cool and finely grinding the entire mass together yielded the cementitious material. This would have provided both a caustic base (the ashes - probably potash [potassium hydroxide] depending on what the critters had been eating) and the meta-kaolin in one fell swoop.
There are some recipes given in "The Aqueduct of Nemausus" by Georg Hauk, a modern telling which describes the process of constructing the aqueduct that supplied water to the Roman colony at Nimes, France, which includes the ever-picturesque Pont du Gard. Among other things, this book made me appreciate the Roman engineers as
project managers and logistics experts. But, it gave recipes for plasters, renders and concretes, as well (as I recall, fermented green figs and sour wine were among the ingredients, though it's probably been 25 years now since I read it). I can't vouch for whether the recipes are correct or will work. The book is best viewed as historical fiction, I think, so some technical details may be amiss and experimental verification is likely in order.
There are modern cement formulations which are aluminum- and magnesium-based, as well as calcium-based. Some formulations can be cured at temperatures only slightly elevated above room temperature (e.g. covered with black sheet plastic on a sunny summer day), and are refractory - very heat resistant. "Low temperature geopolymer setting" or "LTGS" would be a search term to use. Among the experiments I have yet to do is to try to make something refractory from my local clay without initial high firing. This could have both structural uses and be applicable to masonry
heaters - maybe even core linings (i.e. fire brick). This could also be used to make stoneware vessels, roof tiles and the like, if it works. I also have a sample of local shale to play with, and some organic acids (citric, oxalic and acetic) which can reportedly be used, alone or in combination, to "activate" clays (maybe shales, too) for use as cementitious binders.
Hot mix mortars of quicklime were probably more common in times past. There is archaeological evidence which points in this direction, but little written historical documentation from western Europe, since technical knowledge was controlled by largely illiterate craft guilds, verbally passed from master to apprentice. Villard de Honnecourt's work is rare, nearly unique. Rodrigo Gil de Hontanon is later. Neither discuss details of cement or mortar, as best I recall - they were more concerned with stone. I can post up some details or links about hot mix mortars, if anyone cares, but this isn't strictly Roman, so might fit better elsewhere.
But, lime-based mortars and cements are self-healing because of the inverted solubility curve of calcium carbonate. In other words, it is more soluble in water at low temperatures than at higher temperatures. Usually, when we want to make a saturated solution (simple syrup, or salt water, or copper sulfate, or what-have-you) we heat up the water to more easily dissolve the solute. But, calcium carbonate is one of the few substances which works the other way around, and leaves deposits in the kettle or
water heater. Actually, it's even more nuanced than that, but I'm afraid my chemistry is not sufficiently up to snuff to understand, let alone pass on, the details.