Rosetta's scorefunction has gone though many changes over the years. This page documents some of the landmarks.
An introductory tutorial on how to score biomolecules using Rosetta can be found here.
Rosetta has never relied exclusively on a single scorefunction (except maybe in its earliest incarnation). Popular protocols like relax and ab initio use different scorefunctions at different points in their execution. Since the advent of design in Rosetta, most applications stick to a single scorefunction.
See also the Rosetta Canon
Rohl CA, Strauss CE, Misura KM, Baker D (2004) Protein structure prediction using Rosetta. (pubmed link)
Methods in Enzymology.
This paper, often called the Rohl review, is a window into Rosetta's early scorefunction, and remains an excellent reference for early forms of the score function terms. It can be a little hard to find online, but paper photocopies float around most Rosetta labs.
Kuhlman B, Dantas G, Ireton GC, Varani G, Stoddard BL, Baker D (2003)
Design of a novel globular protein fold with atomic-level accuracy. (pubmed link)
Science 302:1364-8
This paper, often called the Top7 paper, is primarily a design paper (see below), but is important for scoring as it introduces sequence-related energy terms (reference energies, p_aa_pp, etc), and is the closest reference for "where score12 came from".
The supplemental is most relevant for scoring.
Leaver-Fay A, O'Meara MJ, Tyka M, Jacak R, Song Y, Kellogg EH, Thompson J, Davis IW, Pache RA, Lyskov S, Gray JJ, Kortemme T, Richardson JS, Havranek JJ, Snoeyink J, Baker D, Kuhlman B (2013)
Scientific benchmarks for guiding macromolecular energy function improvement. (pubmed link)
Methods Enzymol 523:109-43
Leaver-Fay et al. describe OptE, a methodology for using sequence-recovery and rotamer-recovery benchmarks to improve weights sets for scoring functions. This was used in the next paper...
O'Meara MJ, Leaver-Fay A, Tyka M, Stein A, Houlihan K, DiMaio F, Bradley P, Kortemme T, Baker D, Snoeyink J, Kuhlman B (2015)
A Combined Covalent-Electrostatic Model of Hydrogen Bonding Improves Structure Prediction with Rosetta. (pubmed link)
J Chem Theory Comput. 2015;11(2):609-622. PubMed PMID: 25866491
...to generate Talaris2013/4, the current state-of-the-art general purpose Rosetta energy function.
Park H, Bradley P, Greisen Jr. P, Liu Y, Mulligan VK, Kim DE, Baker D, DiMaio F (2016) Simultaneous Optimization of Biomolecular Energy Functions on Features from Small Molecules and Macromolecules. (pubmed link) J Chem Theory Comput. 2016;12(12):6201–6212. PubMed PMID 27766851
Alford RF, Leaver-Fay A, Jeliazko JR, O'Meara MJ, DiMaio FP, Park H, Shapovalov MV, Renfrew PD, Mulligan VM, Kappel K, Labonte JW, Pacella MS, Bonneau R, Bradley P, Dunbrack RL, Das R, Baker D, Kuhlman B, Kortemme T, Gray JJ (2017) The Rosetta all-atom energy function for macromolecular modeling and design.(acs link) J Chem Theory Comput. 2017;13(6):3031-3048
*Rosetta2 / pre-score12 days -- ????
Score12 was the gold standard from the beginning of the Rosetta3 era up until the release of Talaris13. This is substantially similar to the scorefunction discussed in the Top7 paper above. The 12 has no particular meaning - it was the 12th scorefunction listed in the database.
Score12_correct was widely discussed at RosettaCONs for several years running as a collection of terms to improve Score12's performance. It was never adopted wholesale.
Talaris13 was the result of a meeting (held at a hotel named Talaris) where the community used OptE and many new scorefunction tests to try to improve on Score12. It was denoted 13 both as a successor to score12 and because it was developed in 2013.
Talaris14 is an error-correction of Talaris13. One of the hydrogen bonding weights was incorrect. All the weights were re-scaled to more closely match the Rosetta Energy Unit size of score12 - ultimately the units are arbitrary but better comparison with score12 was desired. The YHH_planarity term was added to help control the alcohol hydrogen in tyrosine. This was developed in 2014, but not put into use until 2016.
REF2015 was developed as beta_nov15 and became the default scorefunction in July 2017. Beta_nov16 is under development behind it.