Using K- and R-band imaging of the ELAIS N2 field, we investigate the number counts, clustering, morphology and radio/X-ray emission of extremely red objects (EROs), defined as galaxies with R − K > 5.0. This criterion will select old, passive ellipticals at z > 0.9. To K = 21 we identify a total of 158 EROs in 81.5 arcmin 2 . The ERO number counts are lower than predicted by pure luminosity evolution models, but higher than predicted by current cold dark matter-based hierarchical models. The ERO counts are consistent with a non-evolving model and also with a luminosity evolution model incorporating moderate merging and a decrease with redshift in the comoving number density of passive galaxies (‘M-DE’). We investigate the clustering of the EROs by calculating their angular correlation function, ω(θ ), and obtain a >2σ detection of clustering at K =19‐20 limits. The ω(θ ) amplitude of these EROs is much higher than that of full K-limited samples of galaxies, and is best-fitted by models with a comoving correlation radius r 0 � 10‐13 h −1 Mpc. These results, which are in agreement with Daddi et al., suggest that the intrinsic clustering of at least the brighter EROs is even stronger than that of present-day giant ellipticals. We estimate seeing-corrected angular sizes and morphological types for a K 19.5 subsample of EROs (31 galaxies) and find a ∼3:2 mixture of bulge and disc profiles. Of these EROs ∼ 1 appear to be interacting, disturbed or otherwise irregular, and two are visible mergers. We find the angular sizes of the bulge-profile EROs are consistent with passively evolving ellipticals in the M-DE model, at the expected z ∼ 0.9‐2. The ERO mean radii are smaller than the non-evolving prediction, implying surface brightness evolution. Seven of the 31 bright EROs are detected as F(1.4GHz) 30 µJy radio sources in a VLA survey. The strongest, at 5 mJy, is also a Chandra X-ray detection, and lies at the centre of a significant overdensity of EROs ‐ it is probably an FRI radio galaxy in a z ∼ 1 cluster. Of the other, much fainter, sources, five are point-like and may be weak active galactic nuclei, while the sixth is elongated and aligned with the optical axis of an extended, low-surface brightness ERO, suggesting a powerful but dust-reddened starburst. A possible interpretation is discussed in which the EROs are a mixture of (i) ‘pEROs’, strongly clustered passively evolving giant ellipticals, formed at high redshifts, the oldest EROs and (ii) ‘dsfEROs’, dusty post-interaction galaxies, with a few active starbursts (ULIRGs), and less strongly clustered. With time, the younger dsfEROs are continually assimilated into the ERO class, diluting the clustering and increasing the comoving number density. Both types ultimately evolve into present-day early-type galaxies.