Optimization tasks in computational fluid dynamics (CFD) are as ubiquitous in the automotive industry as CFD applications themselves. Whereas CFD has become an integral part of the car development process, CDF optimization is still in its infancy. This paper reports on our approaches to fluid dynamical optimization tasks. For the purpose of a comparative study of these approaches, we focus on a single, but representative application: shape optimization of a climate channel. The methods employed are black-box algorithms including a multi-objective optimizer, adjoint methods for the calculation of sensitivities and topology optimization for the optimal exploitation of available design space. The paper presents an overview of these methods and rates their respective appropriateness for specific design tasks - in terms of achievable design improvement, numerical cost and integrability into the car development process.