I will present a detailed study of the heavy flavor properties of jets
 produced at the Fermilab Tevatron, including those produced in association
 with W bosons. The study was performed in data sets collected with the CDF
 detector during the 1992-1995 collider run. Jets containing hadrons with
 heavy flavor are selected via the identification of secondary vertices
 or semileptonic decays. Data are compared to a simulation based on $b\bar{b}$
 and $c\bar{c}$ production evaluated with the HERWIG Monte Carlo generator.
 The rate and kinematical properties of jets containing displaced secondary
 vertices can be modeled by tuning the simulation within experimental and
 theoretical uncertainties.
 However, the number of events in which jets contain a soft lepton is
 significantly larger than what is expected for the conventional production
 and semileptonic decay of pairs of hadrons with heavy flavor.