  LISA, the Laser Interferometer Space Antenna, will usher in a new era in
gravitational-wave astronomy. As the first anticipated space-based
gravitational-wave detector, it will expand our view to the millihertz
gravitational-wave sky, where a spectacular variety of interesting new sources
abound: from millions of ultra-compact binaries in our Galaxy, to mergers of
massive black holes at cosmological distances; from the beginnings of inspirals
that will venture into the ground-based detectors' view to the death spiral of
compact objects into massive black holes, and many sources in between. Central
to realising LISA's discovery potential are waveform models, the theoretical
and phenomenological predictions of the pattern of gravitational waves that
these sources emit. This white paper is presented on behalf of the Waveform
Working Group for the LISA Consortium. It provides a review of the current
state of waveform models for LISA sources, and describes the significant
challenges that must yet be overcome.
