With the development of advanced compression ignition (ACI) engines such as the homogeneous charge compression ignition (HCCI) and the reactivity controlled compression ignition (RCCI), the long existing research and motor octane rating for fuels, i.e., RON and MON, might be insufficient to describe fuel reactivity and performance with these new combustion strategies due to their distinctive engine operating conditions. It is also noted that with stringent regulation of CO2 emissions, a detailed knowledge of fuel reactivity is urgently needed for the selection of novel alternative bio-fuels for transportation, and optimization of their engine performance in the future. It is therefore very important to understand the general fuel properties such as reactivity and sensitivity under different ACI operating conditions. In this modeling study, using validated kinetic mechanisms for ignition, different classes of fuels including hydrogen, alkanes (straight and branched) and alcohols have been simulated under typical HCCI engine conditions using detailed chemical kinetics. The crank angle corresponding to 50% total heat release (CA50) was utilized as an indicator of the fuel reactivity, and iso-contours of CA50 were then plotted in engine operating parameter coordinates, such as the intake temperature, and pressure. It is shown that fuels with the same RON/MON could even exhibit both qualitatively and quantitatively different CA50 iso-contours in specific operating regimes, implying the insufficiency of RON/MON as comprehensive metrics of fuel reactivity in ACI strategies. In addition, operating regimes with high and low sensitivity, as well as potential non-monotonic change in fuel reactivity have been identified by the CA50 iso-contour map for all fuels studied. It is also shown that the combustion phasing can increase, decrease, or exhibit non-monotonic changes with equivalence ratio variation, subject to fuel and operating conditions. This study provides useful insights into the control of ACI combustion phasing and the understanding of SI end-gas auto-ignition, as well as implications on the selection of future alternative fuels and the derivation of fuel surrogate models.