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In the effective Ising spin-1/2 antiferromagnetic chain systemBaCo$_2$V$_2$O$_8, the magnetic-field influence is highly anisotropic. Formagnetic fields along the easy axis $c$, the N\'{e}el order is stronglysuppressed already for low fields and an incommensurate order is entered above4 T. We present a detailed study of the magnetic phase diagrams for differentmagnetic field directions, which are derived from magnetization data,high-resolution thermal expansion and magnetostriction measurements as well asfrom the thermal conductivity. Zero-field thermal expansion data reveal thatthe magnetic transition is accompanied by an orthorhombic distortion within the$ab$ plane. Under ambient conditions the crystals are heavily twinned, but thedomain orientation can be influenced either by applying uniaxial pressure or amagnetic field along the [100] direction. In addition, our data reveal apronounced in-plane magnetic anisotropy for fields applied within the $ab$plane. For $H || [110]$, the magnetic field influence on T$_N$ is weak, whereasfor magnetic fields applied along [100], T$_N$ vanishes at about 10 T and thezero-field N\'{e}el order is completely suppressed as is confirmed by neutrondiffraction data. The second-order phase transition strongly suggests a quantumcritical point being present at $H\simeq 10$ T parallel [100], where theN\'{e}el order probably changes to a spin-liquid state.

Magnetic phase diagrams, domain switching and a quantum phase transition of the quasi-1D Ising-like antiferromagnet BaCo2V2O8