Approximation of positive polynomials by sums of squares has important applications to polynomial optimisation. In this talk, I will survey the main recent results achieved on that topic: I will consider positive (respectively, non-negative) polynomials on compact (respectively, unbounded) semi-algebraic sets. I will discuss representations in the associated preorderings (respectively, linear representations in the associated quadratic module). The representation often depends on the dimension of the semi-algebraic set; I will present stronger results in the low dimensional case. I will also highlight special representations when the positive polynomials under consideration are sparse (that is, satisfy some separation and overlap conditions on the variables appearing in the monomials).