Boundary conditions to the compressible Navier-Stokes equations are developed for the case of deformable, generalized coordinates. The general theory is based on a idea of Halpern [SIAM J. Math. Analy., Vol. 22(5), pp. 1256-1283, 1991] which, in the inviscid case, reduces to standard characteristic treatment and thus logically extends the work of Thompson [J. Comput. Phys., vol. 68, pp. 1-24, 1987], Poinsot & Lele [ibid, vol. 101, pp. 104-129, 1992], and Kim & Lee [AIAA J., vol. 42(1), pp. 47-55, 2004]. The issue of well-posedness is considered. The developed boundary conditions are applicable to fluid problems with moving boundaries in inviscid and viscous fluids. Several verification problems are presented to demonstrate accuracy.