The typical problem of extremal combinatorics can be formulated as follows: given a property P and parameter f of combinatorial structures, what is the maximum/minimum of f over all structures having property P. In most of the cases, non-deterministic methods are very succesful in providing the extremal object with the required property. However, there are a few examples where explicit constructions are more effective. They are also important for practical applications, even in cases when the existence of a much better structure is known via the probabilistic method. In this talk we discuss the two approaches through two classic problems of combinatorics: Ramsey- and Turán-type problems.