The Butcher-Oemler effect is the excess of galaxies bluer than the color-magnitude sequence (where most ellipticals/passive galaxies lie) in clusters at z > 0.1 - 0.2 as compared to the richest nearby clusters . Butcher and Oemler were well aware that the fraction of blue galaxies depends on a number of things, including the cluster type, the clustercentric radius considered and the galaxy magnitude limit, as discussed below.
Optical versus X-ray cluster selection - The dependence of the blue fraction on the cluster properties is potentially critical, given that selecting different types of clusters at different redshifts could in principle mimic an evolution. For this reason, it is interesting to ask whether optically and X-ray selected samples of clusters reach similar conclusions regarding the Butcher-Oemler effect [2, 3]. Based on the CNOC (Canadian Network for Observational Cosmology) X-ray-selected cluster sample, an evolution of the blue fraction with redshift, very similar to the original Butcher-Oemler result, has been confirmed [4, 5]. Interestingly, the blue fraction shows no simple trend with cluster X-ray luminosity [2, 3, 6], a point I will discuss later.
Richness - How the blue fraction (fB) depends on cluster richness has been the subject of an extensive study by , who found fB to be higher in poor clusters and lower in rich clusters, and to increase with redshift for all types of clusters. It would be important to verify how fB depends on richness using a clustercentric radial limit that varies with the cluster scalelength, instead of the fixed metric radius (0.7 Mpc) adopted by this study, because this choice could induce a spurious trend with richness by sampling different areas in rich and poor clusters .
Substructure - Possibly the most relevant question of all is how the blue fraction, and the star formation activity in general, depend on cluster substructure, i.e. on the merging/accretion history of the cluster. The exact relation between subcluster merging and blue fraction still needs to be quantified, though there is a tendency for clusters with the highest blue fractions to show signs of recent merging events [8, 9, 2 10]. Based on spectroscopy, there is of course ample evidence for larger fractions of starforming galaxies in substructured than in relaxed clusters. This trend can originate from a higher average SF activity in the smaller (less massive) systems that make up substructured clusters [11, 12], but can also be amplified by starbursts induced by the merger itself [13, 14, 8, 15] as predicted by several theoretical simulations.
Given the dependence of blue fraction on the cluster characteristics, understanding how fB evolves at z > 0.5 is more problematic with the current cluster samples: a very massive cluster at z = 0.8 (MS1054-03) has a blue fraction similar to typical values in clusters at z = 0.4-0.5 , while in other z ~ 1 clusters higher fractions approaching 70-80% have been reported [17, 18].
Two aspects are worth highlighting here. First, we should appreciate that fully understanding (at any given redshift) how the galaxy properties depend upon the cluster properties is very useful in order to uncover how environment affects galaxy evolution. Thus, the dependence of the galactic properties on the cluster characteristics is not a "burden" that is in our way when trying to disclose evolutionary effects. On the contrary, it is in a sense the very thing we are looking for.
Second, the lack of simple correlations between the galaxy properties and the cluster most general (easier to observe) characteristics such as the total X-ray luminosity or the optical richness shows that a single global cluster property of this kind is an insufficient information to characterize the cluster status in a useful way for galaxy evolution studies. More detailed pieces of information are needed, including among others quantitative measurements of the cluster mass, of the ICM local density, the knowledge of the dynamical status of the cluster and its history of accretion of other clusters/groups. In this sense, the wavelength criterion for cluster selection (optical versus X-ray) is not useful on its own, because there is no cluster selection method that is immune from the problem of carefully understanding a posteriori, on a cluster-by-cluster basis, what is the cluster status and history.
Great care is required to compare fB values of different clusters in a meaningful way also because the blue fraction depends on the magnitude limit adopted, on the passband (, see also De Propris in these proceedings) and on the clustercentric radius.  have shown that when looking only at the central core region (typically ~ 0.5 Mpc), no trend with redshift is observed, while the Butcher-Oemler effect is conspicuous outside of the core. The radial distribution of the blue galaxies and its evolution with z must be related to the infall of field galaxies onto the cluster. The declining infall rate onto clusters at lower z is likely to play an important role in the Butcher-Oemler effect, together with the evolution of the average star formation rate in the field galaxies and the decline of star formation in cluster galaxies [5, 4]. The Butcher-Oemler effect and the fact that the galaxy populations in clusters evolve significantly during the last Gyrs are confirmed by the spectroscopic and morphological studies described below. This evolution involves luminous giant galaxies, though probably not the most massive early-type galaxies that populate the top end of the magnitude sequence, as discussed in the next section.