Magnetic-field dependent studies of low-dimensional quantum spin systems yield access to experimental investigations of the generic behavior close to quantum phase transitions. Of particular interest are materials, which realize the XXZ spin-1/2 chain model with anisotropy parameter Δ=Jz/Jxy of the exchange couplings acting either on the z- or the x(y)-spin components. For Δ=0, 1 and ∞, respectively, the exactly solvable XY, Heisenberg and Ising chain models are covered, but real materials are typically located in between these models and there are additional intra- and/or inter-chain couplings. In this contribution, I will present our recent results on model materials which represent experimental realizations of the XXZ spin-1/2 chain model close to the different limits. The spin-1/2 Heisenberg chain is almost ideally realized by Cu(C4H4N2)(NO3)2 and we could study its field-induced quantum phase transition in great detail. In BaCo2V2O8, the Co2+ ions realize effective spin-1/2 chains with pronounced Ising anisotropy. Here, sizable inter-chain couplings cause long-range antiferromagnetic order with complex magnetic-field temperature phase diagrams, but for a particular field direction, we observe the characteristic quantum critical behavior expected for the Ising spin-1/2 chain in transverse magnetic field. In contrast, the Co2+ spins in Cs2CoCl4 are close to the easy-plane limit and we partially observe the characteristic behavior of XY spin-1/2 chains, which is cut off, however, by a complex 3-dimensional order at low temperatures.