"The Mindy Project" (9 p.m., Fox): Fans of the show have patiently waited through a two-month hiatus to find out what's going on with Mindy (Mindy Kaling) and Danny (Chris Messina) who were last seen engaged in a passionate lip-lock. Apparently, sparks are about to fly at Shulman & Associates.
"Inside Amy Schumer" (10:30 p.m., Comedy Central): Headlined by its sweet-faced but potty-mouthed star, this was one of TV's funniest surprise hits last year. So expectations are sky high as it returns for another season of scripted vignettes, stand-up comedy and woman-on-the-street interviews.
"Justified" (10 p.m., FX): Raylan (Timothy Olyphant) takes his war on Darryl Crowe Jr. (Michael Rapaport) to the streets, putting pressure on local criminals as a ploy to get Crowe in custody. Meanwhile, Boyd and Duffy (Walton Goggins, Jere Burns) make an unlikely ally.
Also on Tuesday: