Context. L1642 is one of the two high galactic latitude (vertical bar b vertical bar > 30 degrees.) clouds confirmed to have active star formation. Aims. We examine the properties of this cloud, especially the large-scale structure, dust properties, and compact sources at different stages of star formation. Methods. We present high-resolution far-infrared and submillimetre observations with the Herschel and AKARI satellites and millimetre observations with the AzTEC/ASTE telescope, which we combined with archive data from near-and mid-infrared (2MASS, WISE) to millimetre wavelength observations (Planck). Results. The Herschel observations, combined with other data, show a sequence of objects from a cold clump to young stellar objects (YSOs) at different evolutionary stages. Source B-3 (2MASS J04351455-1414468) appears to be a YSO forming inside the L1642 cloud, instead of a foreground brown dwarf, as previously classified. Herschel data reveal striation in the diffuse dust emission around the cloud L1642. The western region shows striation towards the NE and has a steeper column density gradient on its southern side. The densest central region has a bow-shock like structure showing compression from the west and has a filamentary tail extending towards the east. The differences suggest that these may be spatially distinct structures, aligned only in projection. We derive values of the dust emission cross-section per H nucleon of sigma(e)(250 mu m) = 0.5-1.5 x 10(-25) cm(2)/H for different regions of the cloud. Modified black-body fits to the spectral energy distribution of Herschel and Planck data give emissivity spectral index beta values 1.8-2.0 for the different regions. The compact sources have lower beta values and show an anticorrelation between T and beta. Conclusions. Markov chain Monte Carlo calculations demonstrate the strong anticorrelation between beta and T errors and the importance of millimetre wavelength Planck data in constraining the estimates. L1642 reveals a more complex structure and sequence of star formation than previously known.