Planet Signature Detection

Lightkurve
(Python) A utility for downloading & analyzing light curves and target pixel files from Kepler, K-2, and TESS. The developers are actively adding new analysis tools. (citation: ???)

MulensModel
(Python) Modeling software for microlensing events which can then be used to compare against observed data. (citation: Poleski & Yi 2019)

RVSearch
(Python) Uses models calculated by RadVel (below) to search observations for periodic rv signals. (citation: Rosenthal et al. 2021)

Wotan
(Python) Contains dozens of algorithms for reducing, detrending, and analyzing light curve data. (citation: Hippke et al. 2019)

Compositional and Dynamical Modeling

EXOFASTv2
(IDL) Powerful modeling software capable of modeling a planetary system based on input RV, transit, and astrometric data, as well as characterize the system's host star. Also offers a decent set of tutorials for new users. (citation: Eastman et al. 2019)

petitRADTRANS
(Python) Software for computing transmission and emission spectra of exoplanets. (citation: Molliere et al. 2019)

RadVel
(Python) Convenient Keplerian modeling for exoplanet characterization based on radial velocity data. (citation: Fulton et al. 2018)