  Tensor models and tensor field theories admit a $1/N$ expansion and a melonic
large $N$ limit which is simpler than the planar limit of random matrices and
richer than the large $N$ limit of vector models. They provide examples of
analytically tractable but non trivial strongly coupled quantum field theories
and lead to a new class of conformal field theories. We present a compact
introduction to the topic, covering both some of the classical results in the
field, like the details of the $1/N$ expansion, as well as recent developments.
These notes are loosely bases on four lectures given at the Journ\'ees de
physique math\'ematique Lyon 2019: Random tensors and SYK models.
