In this paper, we give a review of three hohlraum geometries, including cylindrical, octahedral and six-cylinder-port hohlraums, in inertial confinement fusion (ICF) mainly from theoretical side. Every hohlraum has its own strengths and weaknesses. Although there is a problem of drive asymmetry in the cylindrical hohlraums due to some non-ideal factors, the success of ignition is still possible if more laser energy is available beyond the US National Ignition Facility (NIF) in the future. Octahedral hohlraums can provide the high symmetry flux on capsule. However, octahedral hohlraums suffer from several problems due to the complicated three-dimensional plasma conditions inside. And up to now, there is no one target design with the octahedral hohlraums in which each problem can be solved at the same time. Six-cylinder-port hohlraums combine the merits in theory of both cylindrical and octahedral hohlraums to a certain extent. We introduce a target design with good performance by using the six-cylinder-port hohlraums, in which the key issues of concern, such as laser energy, drive symmetry, and laser plasma interaction (LPI), etc, are all balanced.
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