The advent of Fermi is changing our understanding on the radio and γ-ray emission in active galactic nuclei. Unlike pre-Fermi ideas, BL Lac objects are found to be the most abundant emitters in the γ-ray band. However, since they are relatively weak radio sources, most of their parsec-scale structure and their multifrequency properties are poorly understood and/or have not been investigated in a systematic fashion. Here we are analyzing the radio and γ-ray emission properties of a sample of 42 BL Lacs selected with no constraint on their radio and γ-ray emission. Thanks to new Very Long Baseline Array observations at 8 and 15 GHz for the whole sample, we discuss their parsec-scale structure. Parsec-scale radio emission is observed in the majority of the sources at both frequencies. The comparison between our results in radio and gamma-ray bands points out the presence of a large number of faint BL Lacs showing “non-classical” properties such as low source compactness, low core dominance, no gamma-ray emission.