Two events produced by the American Tap Dance Foundation offer looks at tap past and tap present. During the week, "Rhythm Is Our Business" pairs a talented cast of young dynamos and old pros with a big band for a swing-era-style night-club show. On the weekend, "Rhythm in Motion" showcases new choreography by Michelle Dorrance, Derick K. Grant, Max Pollak, Brenda Bufalino, and others - some of the best in the rhythm business. (Theatre at the 14th Street Y, 344 E. 14th St. 866-811-4111. March 19-23 at 7:30 and 9:30 and March 24 at 3.) The final week of the Lincoln Center season offers last chances to catch the company's new pieces: "To Make Crops Grow," which exposes the dark side of village life, and "Perpetual Dawn," in which young love awakens. Bare-chested capoeiristas crouch low and upend themselves, earning approving whistles with their acrobatics and rhythmic smarts. The new work "Fé do Sertão" re-creates a harvest ritual from an arid zone; the score, by the Brazilian composer Marco de Carvalho, draws on the rural baião music of the Sertão region. "Banguela," from 2010, zeroes in on a detail of capoeira practice, a cool interlude of subtle evasions, balances, and fake-outs. (Joyce Theatre, 175 Eighth Ave., at 19th St. 212-242-0800. March 20 at 7:30, March 21-22 at 8, March 23 at 2 and 8, and March 24 at 2.) In "Wunderkammer," the seven members of this contemporary circus troupe from Australia don't wear much more than underwear. That wardrobe choice is a sensual display of flesh, but it's also a mark of up-front informality for a company that slips casually between astonishing feats, jokey stunts, and sudden sparks of beauty. Where else can you see a woman cross the stage by stepping on the heads of standing men? (NYU Skirball Center, 566 LaGuardia Pl. March 20-23 at 8 and March 24 at 3.) In "Being Here," the young choreographer, best known as a dancer with Urban Bush Women, tackles the ravages of mental illness and addiction, staging the kinds of traumatic scenes you might turn away from on the subway. Finding the source of the problem in oppression, her dance seeks to discover remedies through art. March 21-23 at 8.) The pocket-size ballet troupe presents an ambitious program that includes a twentieth-century masterpiece, Antony Tudor's "Dark Elegies" (1937). This small, intense work, set to Mahler's poignant "Kindertotenlieder," is a study in grief expressed through Tudor's anguished, Graham-influenced ballet vocabulary. "A Rugged Flourish" is a vivid new ballet created for the company by the British modern-dance choreographer Richard Alston. Set to Copland's emphatic "Piano Variations," it's a showcase for the troupe's most striking dancer, Steven Melendez. Two eccentric miniatures by the witty James Waring and a new ballet by Gemma Bond, a young British dancer with American Ballet Theatre, fill out the program. In the early afternoon, the troupe presents its short, kid-friendly "Sleeping Beauty." (Florence Gould Hall, 55 E. 59th St. 800-982-2787. Mixed bill: March 22-23 at 7. "Sleeping Beauty": March 23 at 1 and March 24 at 11 A.M., 1, and 3:30.) When this dance was first performed in New York, in 1987, it made an enormous impact. There is nothing stylized about Wim Vandekeybus's choreography: the dancers crash, roll, engage in vigorous, almost violent partnering, and, in the piece's greatest coup de théâtre, hurl large bricks across the stage, seemingly courting disaster. Vandekeybus's Brussels-based company revives the piece. (Michael Schimmel Center for the Arts, Pace University, 3 Spruce St. 866-811-4111. March 22-23 at 7:30.) This new initiative, organized by an Italian-born dance instructor and choreographer who has performed for years with a local company (Michael Mao Dance), brings together a handful of Italian ensembles and a smattering of local troupes with Italian connections. The focus is on middle-of-the-road modern dance, with an emphasis on personal expression and multicultural exchange. Atzewi Dance, from the northern Italian city of Modena, specializes in technically virtuosic, stylish works, often accompanied by electronic scores; Aconcoli Dance, from Milan, has a strong Martha Graham base; the choreographer Alessandra Corona, born in Sardinia, was a longtime dancer with Ballet Hispanico. The American component includes the New York-based Mare Nostrum and students from the Talent Unlimited High School, performing a tarantella. (Julia Richman, 317 E. 67th St. 646-387-8979. March 22 at 7:30.) The series, held in a tiny theatre tucked beneath the Museum of Arts and Design, hosts an evening of dance that covers a wide range of styles. Young dancers from American Ballet Theatre's studio ensemble ABT II - a stepping stone between school and company - perform an excerpt from Alexei Ratmansky's "Carnaval des Animaux," made for San Francisco Ballet in 2003. Basil Twist - a puppeteer-magician - will do a duet with one of his creations, a twenty-inch puppet named Stickman. The all-female hip-hop crew Decadance and the modern dancer David Neumann also perform. (2 Columbus Circle. Audiences are increasingly drawn to examining the nuts and bolts of artistic creation, and the Harkness Dance Festival obliges with its "Stripped/Dressed" series. March 22-23 at 8 and March 24 at 3.) Jones's company marks its thirtieth season with a two-week season at the Joyce, where it last performed in 2009. The two programs contain a wide range of works, spanning three decades. Both are filled with classical music - including Mendelssohn's Octet and Schubert's "Death and the Maiden" - played live by the Orion String Quartet. The oldest piece, "Continuous Replay" (Program A), is a reworking of "Hand Dance," choreographed in 1977 by Jones's late partner, Arnie Zane; it uses forty-five discrete hand gestures. The newest composition, "Story" (Program B), is a continuation of the rigorous time-based methods Jones explored in last year's "Story/Time." In that work, Jones told one-minute stories as his dancers noodled around him for predetermined periods of time. March 26 at 7:30. Through April 7.)