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We summarize recent numerical results on the control of the star formationefficiency (SFE), addressing the effects of turbulence and the magnetic fieldstrength. In closed-box numerical simulations, the effect of the turbulent Machnumber $\Ms$ depends on whether the turbulence is driven or decaying: In drivenregimes, increasing $\Ms$ decreases the SFE, while in decaying regimes theconverse is true. The efficiencies in non-magnetic cases for realistic Machnumbers $\Ms \sim 10$ are somewhat too high compared to observed values.Including the magnetic field can bring the SFE down to levels consistent withobservations, but the intensity of the magnetic field necessary to accomplishthis depends again on whether the turbulence is driven or decaying. In thiskind of simulations, a lifetime of the molecular cloud (MC) needs to beassumed. Further progress requires determining the true nature of theturbulence driving and the lifetimes of the clouds. Simulations of MC formationby large-scale compressions in the warm neutral medium (WNM) show that theclouds' initial turbulence is produced by the accumulation process that formsthem, and that the turbulence is driven for as long as this process lasts,producing realistic velocity dispersions and also thermal pressures in excessof the mean WNM value. In simulations including self-gravity, but neglectingthe magnetic field and stellar energy feedback, the clouds never reach anequilibrium state, but rather evolve secularly, increasing their mass andgravitational energy until they engage in generalized gravitational collapse.However, local collapse events begin midways through this process, and produceenough stellar objetcs to disperse the cloud or at least halt its collapsebefore the latter is completed.Comment: 8 pages, 2 postscript figures, invited talk in IAU Symposium 237,  "Triggered Star Formation in a Turbulent ISM", 14-18 August, Prague, Czech  Republic, eds. B. Elmegreen & J. Palous. Abstract abridge

Molecular cloud turbulence and the star formation efficiency: enlarging the scope