We have completely mapped the Galactic globular cluster NGC 1851 with large-field, ground-based VI CCD photometry and pre-repair HST/WFPC1 data for the central region. The photometric data set has allowed a V vs. (V-I) colour-magnitude diagram for ~ 20500 stars to be constructed. >From the apparent luminosity of the horizontal branch (HB) we derive a true distance modulus (m-M)_0 = 15.44 +/- 0.20. An accurate inspection of the cluster's bright and blue objects confirms the presence of seven ``supra-HB'' stars, six of which are identified as evolved descendants from HB progenitors. The HB morphology is found to be clearly bimodal, showing both a red clump and a blue tail, which are not compatible with standard evolutionary models. Synthetic Hertzsprung-Russell (HR) diagrams demonstrate that the problem could be solved by assuming a bimodal efficiency of the mass loss along the red giant branch (RGB). With the aid of Kolmogorov-Smirnov statistics we find evidence that the radial distribution of the blue HB stars is different from that of the red HB and sub-giant branch (SGB) stars. We give the first measurement of the mean absolute I magnitude for 22 known RR Lyr variables ( = 0.12 +/- 0.20 mag at a metallicity [Fe/H] = -1.28). The mean absolute V magnitude is = 0.58 +/- 0.20 mag, and we confirm that these stars are brighter than those of the zero-age HB (ZAHB). Moreover, we found seven new RR Lyr candidates (six ab type and one c type). With these additional variables the ratio of the two types is now N_c/Nab = 0.38. >From a sample of 25 globular clusters a new calibration for Delta V_bump() HB as a function of cluster metallicity is derived. NGC 1851 follows this general trend fairly well. From a comparison with the theoretical models, we also find some evidence for an age-metallicity relation among globular clusters. We identify 13 blue straggler stars, which do not show any sign of variability. The blue stragglers are less concentrated than the subgiant branch stars with similar magnitudes for r>80 arcsec. Finally, a radial dependence of the luminosity function, a sign of mass segregation, is found. Transforming the luminosity function into a mass function (MF) and correcting for mass segregation by means of multi-mass King-Michie models, we find a global MF exponent x_0=0.2+/- 0.3. Based on observations made at the European Southern Observatory, La Silla, Chile, and archive HST observations retrieved through the {sc starview