Virgil Elliott, www.virgilelliott.com

The darkening effect of turpentine is well known in conservation circles. It isn’t a matter of opinion or guesswork; it’s a fact.

Oil paint doesn’t really need to be thinned with any volatile solvent. One might get by with it if one only adds a little bit from an eyedropper and mixes it in well on the palette with a palette knife, but dipping the brush into it and mixing it that way is too imprecise to be considered optimal, because the likelihood of getting too much in one spot or another is too great. And that’s the way most people do it. Thinning beyond a certain point reduces the binding power of vegetable oils, so the question then is how far is too far. The only way to be sure is not to thin the paint with solvent at all. 

Paints ground on roller mills or pebble mills are already lower in oil content than the hand-mulled paints used by the Old Masters, so it stands to reason that we can add a drop or two of linseed oil to a good-sized pile of paint that needs to be softer, and mix it in well, without ending up with problems from too much oil in the paint. And that way there’s less disparity in surface gloss than when the paints are thinned with solvent, which makes the paint dry more matte.

Darren Rousar, Sight-Size.com:

First off, Mineral Spirits are a petroleum based distillate. As such it is relatively new to the artist’s scene and was originally used by artists as a solvent to clean brushes. Commercial paint manufacturers (as in house paint) use MS as well. IMO, MS is a stronger ‘thinner’ than turp.

OMS (odorless mineral spirits) is MS but with various aspects of it removed (like sulphur) to make it more nose friendly. OMS cannot dissolve certain medium additives.

Turpentine is a resin distillate from pine trees and is the more traditional artist’s thinner and additive to mediums.

Turpentine, when used to thin pigment for an imprimatura, presents no problems generally. When using turp thinned pigments over an imprimatura it is possible that one could remove some of the imprimatura layer with the brush. If this aspect is bothersome, there are more or less three alternatives. One is the tone your ground. A toned ground has colored pigment mixed within the ground layer itself. As this is suspended in oil it is ‘locked’ in and will not likely come off. Using your medium as your imprimatura ‘thinner’ would lock it in as well but then this underlayer may be too fat. Alternatively (and perhaps not a really great one at that) one could thin their imprimatura layer with retouch varnish.
I am sure this last one will give many pause. 

AFAIK, the only problem with turp or MS when used to thin a paint mixture (either in an imprimatura or the initial layers of the painting) is a thinning of the oil which binds the pigment. This may be a problem only in that the dried paint may not bond well to the surface. But a layer painted like this is a ‘lean’ layer. I am not aware of any studies showing that this is bad for the painting in the long run. Perhaps others are aware of such studies?

Layering, either intentionally or simply via the act of multi-session painting is always done fat over lean when using oil paint. ‘Lean’ here either means paint straight from the tube or more commonly paint thinned with something other than a fat (oil).