In this talk I revisit current issues in semi-analytic models by 
comparing the predictions by GalICS to the latest observations of the 
abundance ratios in elliptical galaxies, the color bimodality, the 
passive fraction in groups , as well as to the galaxy mass function 
and the specific star formation rate (sSFR) evolution over cosmic 
time. In particular, I explore a range of star formation prescriptions 
and (halo- versus stellar mass-) quenching models. 

"Standard" models predict an excess of red, passive and alpha-enhanced 
population (satellite) galaxies at masses ~ 10^10 Msun.  Whilst both 
the halo- and the mass-quenching models broadly match the present-day 
mass functions, a disagreement with data becomes evident at high 
redshift, in terms of a lack of massive galaxies and an excess of 
lower mass objects.  At lower masses the models predict an excess of 
(passive) galaxies, as well as a milder evolution at z<2 in the number 
density, at variance with observations and irrespective of the adopted 
quenching model. A better match is achieved by empirically forcing the 
model galaxies to obey to the observed sSFR evolution. This empirical 
solution brings the predicted passive-fraction and the colors in 
better agreement with data and shows that many of the current problems 
in semi-analytic models are rooted in the prescriptions for the gas 
accretion/cooling and the star formation. 

In the final part of the talk I will show preliminary results from 
analytical toy models aimed at explaining the cosmic run of the sSFR.