The standard cosmological model has been established  and its parameters are now measured with unprecedented precision. However, there is a big difference between modelling and understanding.  The next decade  will see the era of large surveys; a large coordinated effort of the scientific community in the field  is on-going to map the cosmos producing an  exponentially growing amount of data. This will shrink the statistical errors. But precision is not enough: accuracy is also crucial.   Systematic effects may be in the data but may also be in the model used in their interpretation.  I will present a small selection of examples where I explore  approaches to help the  transition from precision to accurate cosmology. This selection is not meant to be exhaustive or representative, it just cover some of the problems I have been working on recently.