Seismic inversion is inherently ill-posed, and needs proper regularisation for producing a well-behaved model estimate. From the statistical point of view, the minimisation problem with a model constraint is equivalent to maximising a conditional probability, given the data measurements. Any probability function that can appropriately describe the behaviour of the expected model can be adopted as a regularisation in the inversion. Regularisation can be a model constraint used together with the data fitting in an objective function and can be applied directly to the geophysical operator. Least-squares inversion of data fitting can be interpreted as maximising the probability of data or errors with a Gaussian distribution, and the least-squares inversion plus various regularisation can be interpreted as maximising the posterior distribution of the model solution. This chapter explains and compares three various regularisations namely Lp norm constraint, Maximum entropy constraint and Cauchy constraint.