The ATLAS Inner Detector tracking trigger at 13 TeV in LHC Run-2 and new developments on standard and unconventional tracking signatures for the upcoming LHC Run-3

The performance of the Inner Detector tracking trigger of the ATLAS experiment at the LHC is evaluated for the data taking period of Run 2 (2015-2018). The Inner Detector tracking was used for the muon, electron, tau and b-jet triggers, and its high performance is essential for the ATLAS physics program such as precision measurements of the Standard Model and searches for new physics. The application of Inner Detector tracking is planned to be significantly expanded for Run 3. For the first time, full-detector tracking will be utilized for signatures with jets and missing transverse momentum and dedicated triggers with unconventional tracking will be utilized to identify massive long-lived particles with ``displaced'' and ``disappearing'' track signatures. Several improvements have been developed to meet computing resource limitations.