ThreeBest projection problems related to the Chebyshev’s criterion are considered. The first problem, finding an ideal projection using the Chebyshev’s criterion, includes two variants of the Postel projection. The second problem introduces Chebyshev's theorem for conformal projections, accompanied by a proof based on the extremal properties of harmonic and subharmonic functions. A formula for calculating the value of the Chebyshev’s criterion for an arbitrary mapping region is provided. The third problem focuses on the Markov projection, demonstrating that the problem of finding the best conic projection cannot be solved within the domain of twice continuously differentiable functions. The projection formulae are determined by the method currently used for constructing splines.