Desorption induced by electronic transitions (DIET) and its variant DIMET (M = 'Multiple'), are among the simplest possible "reactions" of ad-species involving ultra-short lived electronically excited states at surfaces. The non-adiabatic bond-cleavage can be enforced, for example, with laser irradiation or with electrons or holes emitted from the tip of a scanning tunnelling microscope (STM). The transient creation of excited intermediates can proceed directly (localised to the adsorbate-substrate complex), or indirectly (i.e., through the substrate). To understand the basic processes, simple one-mode two-state "toy models" such as the Menzel-Gomer-Redhead (MGR) or the Antoniewicz scenarios have proven very useful in the past. We adopt and extend MGR- and Antoniewicz-type models together with numerically exact open-system density matrix theory to address a few actual problems/experiments in DI(M)ET: (1) Direct, laser-induced desorption of H(D) from Si(100) surfaces which has been realised in the continuous-wave DIET regime only recently [T. Vondrak and X.-Y. Zhu, Phys. Rev. Lett., 1999, 82, 1967], is studied and compared to so-far hypothetical femtosecond laser desorption. The possibility of controlling the reaction by shaping the laser pulses is addressed. (2) For the same system, temperature effects are studied for electron- or hole-stimulated desorption with an STM [T. C. Shen, C. Wang, G. C. Abeln, T. R. Tucker, J. W. Lyding, Ph. Avouris and R. E. Walkup, Science, 1995, 268, 1590; C. Thirstrup, M. Sakurai, T. Nakayama and K. Stokbro, Surf. Sci., 1999, 424, L329]. A modified version of Gadzuk's "sudden transition and averaging" approach is adopted which accounts for temperature dependent excited state lifetimes. (3) For photodesorption of NO from Pt(111), based on quantum dynamical simulations possible experimental tests involving static electric fields are suggested to address the relevance of the recently challenged [F. M. Zimmermann, Surf. Sci., 1997. 390, 174], "negative ion resonance" model of the Antoniewicz type.