In this paper, definitions, units (SI and Gaussian) and some measurement techniques of the magnetoelectric (ME) effects are clarified. The tensor forms of the linear ME effect are given for the 58 ME point groups, comprising also numerous corrections with respect to errata in former published tables. A new dynamic technique for detecting the bilinear ME effect with strikingly enhanced sensitivity is proposed and applied to the measurement of β333(T) of Cr-Cl boracite, allowing two magnetic phase transitions to be clearly evidenced, at 9.7 K (±0.1 K) and at 13.5 K (±0.1 K). It is proposed that in that range of temperature, the ferroelectric phase of Cr-Cl boracite is antiferromagnetic with Shubnikov point group mm2.