We discuss the results of a study of restricted solid-on-solid model Hamiltonians for fee (110) surfaces. These models are simple modifications of the exactly solvable body-centered solid-on-solid model, and are able to describe a (2x1) missing-row reconstructed surface as well as an unreconstructed surface. They are studied in two different ways. The first is by mapping the problem onto a quantum spin-1/2 one-dimensional Hamiltonian of the Heisenberg type, with competing (SiSjz)-S-z couplings. The second is by standard two-dimensional Monte Carlo simulations. We find phase diagrams with the following features, which we believe to be quite generic: (i) two flat, ordered phases (unreconstructed and missing-row reconstructed); a rough, disordered phase; an intermediate disordered flat phase, characterized by monoatomic steps, whose physics is shown to be akin to that of a dimer spin state. (ii) A transition line from the (2x1) reconstructed phase to the disordered flat phase showing exponents that appear to be close, within our numerical accuracy, to the two-dimensional Ising universality class. (iii) A critical (preroughening) line with variable exponents, separating the unreconstructed phase from the disordered flat phase. Possible signatures and order parameters of the disordered flat phase are investigated.