  We present LAISS (Lightcurve Anomaly Identification and Similarity Search),
an automated pipeline to detect anomalous astrophysical transients in real-time
data streams. We deploy our anomaly detection model on the nightly ZTF Alert
Stream via the ANTARES broker, identifying a manageable $\sim$1-5 candidates
per night for expert vetting and coordinating follow-up observations. Our
method leverages statistical light-curve and contextual host-galaxy features
within a random forest classifier, tagging transients of rare classes
(spectroscopic anomalies), of uncommon host-galaxy environments (contextual
anomalies), and of peculiar or interaction-powered phenomena (behavioral
anomalies). Moreover, we demonstrate the power of a low-latency ($\sim$ms)
approximate similarity search method to find transient analogs with similar
light-curve evolution and host-galaxy environments. We use analogs for
data-driven discovery, characterization, (re-)classification, and imputation in
retrospective and real-time searches. To date we have identified $\sim$50
previously known and previously missed rare transients from real-time and
retrospective searches, including but not limited to: SLSNe, TDEs, SNe IIn, SNe
IIb, SNe Ia-CSM, SNe Ia-91bg-like, SNe Ib, SNe Ic, SNe Ic-BL, and M31 novae.
Lastly, we report the discovery of 325 total transients, all observed between
2018-2021 and absent from public catalogs ($\sim$1% of all ZTF Astronomical
Transient reports to the Transient Name Server through 2021). These methods
enable a systematic approach to finding the "needle in the haystack" in
large-volume data streams. Because of its integration with the ANTARES broker,
LAISS is built to detect exciting transients in Rubin data.
