  With wide-field phased array feed technology, the Australian Square Kilometre
Array Pathfinder (ASKAP) is ideally suited to search for seemingly rare radio
transient sources. The Commensal Real-time ASKAP Fast Transient (CRAFT) Survey
Science Project has developed instrumentation to continuously search for fast
radio transients (duration $\lesssim$ 1 second) with ASKAP, with a particular
focus on finding and localising Fast Radio Bursts (FRBs). Of particular
interest are Fast Radio Bursts (FRBs). Since 2018, the CRAFT survey has been
searching for FRBs and other fast transients by incoherently adding the
intensities received by individual ASKAP antennas, and then correcting for the
impact of frequency dispersion on these short-duration signals in the resultant
incoherent sum (ICS) in real-time. This low-latency detection enables the
triggering of voltage buffers, which facilitates the localisation of the
transient source and the study spectro-polarimetric properties at high time
resolution. Here we report the sample of 43 FRBs discovered in this CRAFT/ICS
survey to date. This includes 22 FRBs that had not previously been reported: 16
FRBs localised by ASKAP to $\lesssim$ 1 arcsec and 6 FRBs localised to
approximately 10 arcmin. Of the new arcsecond-localised FRBs, we have
identified and characterised host galaxies (and measured redshifts) for 11. The
median of all 30 measured host redshifts from the survey to date is z = 0.23.
We summarise results from the searches, in particular those contributing to our
understanding of the burst progenitors and emission mechanisms, and on the use
of bursts as probes of intervening media. We conclude by foreshadowing future
FRB surveys with ASKAP using a coherent detection system that is currently
being commissioned.
