Scholary papers describing the methodology
The mvtnorm package implements methods to evaluate the probability, density, and quantile functions of the multivariate normal and t distributions. For the general case, tailored Monte Carlo methods described by Genz and Bretz (2009) are applied; for the bivariate normal the exact approach by Miwa, Hayter, and Kuriki (2003) is available as an alternative.
 T. Miwa, A. J. Hayter and S. Kuriki. “The Evaluation of General Non-centred Orthant Probabilities”. In: Journal of the Royal Statistical Society, Series B: Methodology 65 (2003), pp. 223–234. DOI: 10.1111/1467-9868.00382.
 A. Genz and F. Bretz. Computation of Multivariate Normal and t Probabilities. Vol. 195. Lecture Notes in Statistics. Heidelberg, Germany: Springer-Verlag, 2009.