Cells have to sense and respond to changing environmental conditions. Specifically, to maintain the living state the underlying signal transduction networks have to be sensitive with respect to vital signals while remaining robust with respect to perturbations that could potentially compromise homeostasis. However, the molecular mechanisms leading to the emergence of sensitivity and robustness are still poorly understood. In this talk, I will argue that both properties, in the form of ultrasensitivity and concentration robustness, may already arise in comparably simple signaling systems such as covalent modification cycles or bacterial two-component systems. Starting with the classical Goldbeter-Koshland model, which predicts that ultrasensitivity may result from covalent modification of a substrate by a pair of antagonistic converter enzymes, I show that a similar behavior may also arise in covalent modification systems with a bifunctional enzyme. Interestingly, the latter systems may, in addition, exhibit concentration robustness, i.e. under certain conditions the system output becomes independent of the system components (enzyme and substrate concentrations) which may help compensating variations in the system response due to cell-to-cell fluctuations of protein copy numbers. Concentration robustness has also been observed in bacterial two-component systems with a bifunctional sensor kinase raising the question whether such systems would also exhibit ultrasensitivity to input signals. I show that this, indeed, possible if the input signal reciprocally affects multiple activities of the sensor kinase.