We look at observational constraints on the thawing class of scalar field models proposed to explain the late-time acceleration of the universe. Using the recently introduced ‘Statefinder hierarchy’, we compare these thawing class of models with other widely studied dark energy (and modified gravity) models to check the underlying parameter degeneracies. We put constraints on the deviations of these thawing models from the canonical Λ cold dark matter (ΛCDM) model using a large class of observational data, e.g. the Type Ia supernova (SN) data, the baryon acoustic oscillation data, the cosmic microwave background data and data from the measurements of the Hubble parameter using red-envelope galaxies. We also forecast constraints using a simulated data set for the future Joint Dark Energy Mission (JDEM) SN survey. Our study shows that, although with current data it is difficult to distinguish different thawing models from ΛCDM, a future JDEM-like mission would be able tell apart thawing models from ΛCDM for currently acceptable values of Ωm0.