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Mergers are predicted in all cosmological models involving cold dark matter (CDM) to be one of the dominant channels whereby galaxies accrete mass. In this paper, we present a detailed analysis of predicted galaxy–galaxy merger fractions and rates in the Millennium simulation and compare these with the most up to date observations of the same quantities up to   z ∼ 3 . We carry out our analysis by considering the predicted merger history in the Millennium simulation within a given time interval, as a function of stellar mass. This method, as opposed to pair fraction counts, considers mergers that have already taken place, and allows a more direct comparison with the observed rates and fractions measured with the concentration‐asymmetry‐clumpiness (CAS) method. We examine the evolution of the predicted merger fraction and rate in the Millennium simulation for galaxies with stellar masses   M  ★ ∼ 10 9 –10 12  M ⊙  . We find that the predicted merger rates and fractions match the observations well for galaxies with   M  ★  &gt; 10 11  M ⊙   at   z  &lt; 2 , while significant discrepancies occur at lower stellar masses, and at   z  &gt; 2  for   M  ★  &gt; 10 11  M ⊙   systems. At   z  &gt; 2 , the simulations underpredict the observed merger fractions by a factor of 4–10. The shape of the predicted merger fraction and rate evolutions are similar to the observations up to   z ∼ 2 , and peak at  1 &lt;  z  &lt; 2  in almost all mass bins. The exception is the merger rate of galaxies with   M  ★  &gt; 10 11  M ⊙  , which remains high at   z  &lt; 1.5 . We discuss possible reasons for these discrepancies, and compare different realizations of the Millennium simulation to understand the effect of varying the physical implementation of feedback. We conclude that the comparison is potentially affected by a number of issues, including uncertainties in interpreting the observations and simulations in terms of the assumed merger mass ratios and merger time‐scales. The differences between the observations and simulation results might also be due to problems in the modelling of star formation in the simulation, which produces redder and less biased galaxies than observed, particularly for galaxies with stellar masses   M  ★  &lt; 10 11  M ⊙  . Finally, our findings may also be related to other CDM problems, including the lack of massive galaxies with   M  ★  &gt; 10 11  M ⊙   at   z  &gt; 1 , and a lack of merger events between lower mass galaxies.

A comparison of galaxy merger history observations and predictions from semi‐analytic models