This review summarizes the state of the art of plasma diagnostics on atmospheric pressure plasmas formed at characteristic length scales of approximately 1 mm or smaller and identifies challenges and prospects. Both plasmas generated in confined geometries, so-called microplasmas, as well as discharge filaments occurring in commonly filamentary plasmas, e.g. microdischarges in dielectric barrier discharges are covered. In spite of the differences between microplasmas which often obtain a quasi steady-state and single microdischarges or filaments which are self-limited in space and time and thus intrinsically transient, both face very similar diagnostic challenges of which two are immediately apparent: the high collisionality which requires adaptations of standard plasmas diagnostics often developed for low-pressure plasmas, and the requirements on high spatial resolution due to the strong gradients in plasma properties. The complexity of the plasma generation and the physical and chemical properties of the above-mentioned plasmas requires the knowledge of an extensive series of different parameters to obtain a full characterization. As the results of the diagnostics are not always unambiguous and require a detailed understanding of plasma physics and chemistry, a summary of the main properties and pecularities of high-pressure plasmas is included in this review.