  Knowledge of molecular structure is paramount in understanding, and
ultimately influencing, chemical reactivity. For nearly a century, diffractive
imaging has been used to identify the structures of many biologically-relevant
gas-phase molecules with atomic (i.e. Angstrom, A; 1 A = 10$^{-10}$ m) spatial
resolution. Unravelling the mechanisms of chemical reactions requires the
capability to record multiple well-resolved snapshots of the molecular
structure as it is evolving on the nuclear (i.e. femtosecond, fs; 1 fs =
10$^{-15}$ s) timescale. We present the latest, state-of-the-art ultrafast
electron diffraction methods used to retrieve the molecular structure of
gas-phase molecules with Angstrom and femtosecond spatio-temporal resolution.
We first provide a historical and theoretical background to elastic electron
scattering in its application to structural retrieval, followed by details of
field-free and field-dressed ultrafast electron diffraction techniques. We
discuss the application of these ultrafast methods to time-resolving chemical
reactions in real-time, before providing a future outlook of the field and the
challenges that exist today and in the future.
