A massive bombing by the Islamic State group outside a popular ice cream parlour in central Baghdad and a rush-hour car bomb in another downtown area have killed at least 31 people, including an Australian girl.
Later in the day on Tuesday, bombings in and around the Iraqi capital killed seven more people.
The attacks come as IS militants are steadily losing territory to US-backed Iraqi forces in the battle for Mosul, the country's second-largest city.
The Sunni extremists are increasingly turning to insurgency-style terror attacks to distract attention from their losses.
The night-time attack outside the ice cream parlour in the bustling Karrada neighbourhood killed 17 people and wounded 32, police said.
A 12-year-old schoolgirl from Victoria was reportedly among the dead.
Zaynb Al-Harbeya, from Thomastown in Melbourne, was at the parlour with her uncles when she was killed in the car bomb explosion, Nine Network reports.
The girl was on a short trip to Iraq with her parents to visit her sick grandfather.
A closed-circuit camera captured the moment of the explosion, the video showing a busy downtown avenue with cars driving down the street when the blast strikes.
A huge fireball engulfs a building, causing cars to scramble to get away.
Other videos of the attack posted on social media show wounded and bloodied people crying for help on the footpath outside the ice cream parlour.
In the second attack, an explosives-laden car went off during rush hour near the state-run Public Pension Office in Baghdad's busy Shawaka area, killing 14, a police officer said. At least 37 people were wounded in that attack, he added.
In separate online statements, IS claimed responsibility for the two attacks, saying its suicide bombers targeted gatherings of Shi'ites.
Later on Tuesday, seven people died and 19 were wounded in four separate bombings in and around Baghdad, officials said.
The attacks targeted commercial areas and a patrol of Sunni anti-IS tribal fighters, they said. No group immediately claimed those attacks.
The attacks came just days into the holy month of Ramadan when Muslims fast during daylight hours.
After sundown, families break their fast and Baghdad's restaurants and cafes quickly fill up with people staying up long into the night.
During Ramadan last year, another section of Karrada was hit by massive suicide bombing that killed almost 300 people, the deadliest single attack in the Iraqi capital in 13 years of war. The attack was also claimed by IS.
