IU took her first leading role in a television series in 2013, playing the title role in You Are the Best!. Her character was described as a "loser" who is seemingly average in every way except for her daring and bright personality, which helps her to overcome hardships. Despite the worries of casting someone who is better known as a singer in the role, director Yoon Sung-sik decided to cast IU after seeing her performance in Dream High and thought that she suited the image he had envisioned for the character. Her co-stars Go Doo-shim and Lee Ji-hoon, as well as the production crew, praised her performance, especially during emotional scenes. As the series progressed, IU's performance garnered positive critical reviews despite early reservations shown about her casting, with the viewership ratings reaching a peak of 30.8%. She was nominated for the Excellence in Acting Award (Best Actress in a Serial Drama) at the 2013 KBS Drama Awards. For the drama, she released a recording with her co-star Jo Jung-suk of her self-composed duet, "Beautiful Song" (예쁘다송), which was not included on the official soundtrack.

In the same period, IU released her second Japanese extended-play album, Can You Hear Me?, featuring her first original Japanese songs. Two tracks from the album were released as singles; "Beautiful Dancer" and "New World" peaked at number 66 and 76 respectively on the Billboard Japan Hot 100.] Rolling Stone Japan gave the album a positive review, highlighting "Beautiful Dancer" and "Truth" as stand-out tracks. In an interview with Oricon, IU recalled how shocked and touched she was to receive "Beautiful Dancer" and "Truth" from R&B producers Jimmy Jam and Terry Lewis. Her next Japanese single, "Monday Afternoon", was released on September 11, 2013, debuting at number 27 on Billboard Japan Hot 100 chart and number 9 on Japan's Oricon Daily Chart.

Almost two years after Last Fantasy, IU released her third studio album, Modern Times, on October 8, 2013. It was described to be "a big shift from the young singer's K-pop roots" that showcased a "more mature and sophisticated sound and image" than her previous work. IU composed and wrote two out of the album's 13 tracks, which ranged from swing to jazz, bossa nova, Latin pop and folk genres. The diversity of jazz styles and the mix of collaborative tracks were highlighted in reviews by Billboard and The Korea Herald. Modern Times debuted at number one on the Gaon Album Chart, while seven of its tracks achieved top ten positions on the Gaon Digital Chart with the lead single, "The Red Shoes" (분홍신), placing in the number one position. Similarly, the album debuted number four on Billboard's World Albums Chart, with twelve tracks in the K-pop Hot 100 chart. The album was ranked number two on Billboard's "25 Greatest K-Pop Albums of the 2010s" list.]

On the second week of her promotional activities for Modern Times, IU decided to join the romantic-comedy series Bel Ami. She played the "quirky" and "playful" role of Kim Bo-tong, a carefree girl in her twenties who has had an unrequited crush on the male protagonist since high school. For her performance, IU was nominated in the Outstanding Korean Actress category at the 2014 Seoul International Drama Awards. In support of Modern Times, IU held her second concert tour with three shows which took place on November 23–24, 2013, at Kyung Hee University's Peace Hall in Seoul and ended on December 1, 2013, at KBS Hall in Busan. Promotions for Modern Times progressed into 2014 with IU performing in Hong Kong for the first time in a solo concert. A repackaged version of Modern Times, titled Modern Times — Epilogue, was released on December 20, 2013, with two additional tracks: "Friday" (금요일에 만나요) and "Pastel Crayon" (크레파스). Her self-composed track, "Friday", was originally intended to be included in Modern Times but was later released as the lead single of Modern Times — Epilogue. Described as a "mid-tempo, bossa nova number", "Friday" held the number one position on the Billboard Korea K-pop Hot 100 chart for two weeks after release. The lead single was successful on the Gaon Digital Chart, peaking at number one, and became the tenth best-selling digital single of 2014.