Context. Dippers are typically low-mass, pre-main-sequence stars that display dips in their light curves. These dips have been attributed to dusty warps that form in the inner part of the disk. Aims. Our goal is to derive the characteristics of dipper stars in Taurus to assess the physical mechanisms that induce dipper light curves. Methods. We used the light curves of the fourth and thirteenth campaigns of K2 to select a dipper sample among 179 members and possible members of the Taurus star-forming region based on the light-curve morphology. We studied the periodicities by combining periodograms with wavelet analysis and derived the stellar parameters of the sample from the photometry. We also studied the morphology of the photometric dips. Results. We find a dipper occurrence of ~30% in disk-bearing stars observed with K2 that were identified visually by us. This represents a lower limit to their true occurrence, on the one hand because they are ephemeral, and on the other because there are detection limits. About half of the dippers are aperiodic, and most of these are dominated by another type of variability. The chosen sample is of late spectral type (K/M), low mass (mostly <1 M⊙), and moderate mass accretion rates and has periods of a few days. We observed a transient dipper over a few rotation cycles and observed a dipper with a changing period. The structure of the dips can be complex and varies strongly over timescales of down to one stellar rotation. The corotation radii are located at a few stellar radii, and the temperatures at corotation allow dust survival. Many of the systems are seen at moderate to high inclination. We find that the angular extension of the dusty structure producing the dips is correlated with the stellar period. Conclusions. Magnetospheric accretion, which causes an accretion column and its base to occult the star, can explain most of the observed light curves. Although compatible with the model, many of the stellar inclination angles are moderate and do not exclude mechanisms other than the occultation by an inner disk warp to account for dipper light curves.