She is being accused of using state-controlled banks to finance popular social programmes without revealing she was doing so.
Alarm bells started ringing over her Government's creative accounting in 2013.
A prime example is a flagship programme for Rousseff's Government called the Bolsa Familia, or Family Allowance - in which the Government gives cash to poor Brazilian families, provided they send their children to school and ensure they get vaccinations.
Typically, authorities give the money to a bank, which distributes it to families. The bank started complaining from 2013 that it wasn't getting regular payments from the Government and was having to use its own money to make the payments. In Portuguese, this is called "pedaling". Actually, it was more like running up a giant overdraft. In 2014, the problem got worse. There were tens of billions of dollars in late payments for programmes like these that the banks were left paying for.
Rousseff's accusers say she did this so she could spend more money on vote-winning social programmes in 2014 - the year in which she narrowly won reelection. It was only after her victory that she admitted to Brazilians that the economy was in trouble.
"If it had not been for this electoral fraud, she would not have been re-elected," said Gil Castello Branco, a former government economist and founder of Open Accounts, a nonprofit group in Brasilia which monitors public spending.
What does Rousseff's defence say?
"Pedaling is nothing more than a delay of payments," said Ricardo Ribeiro, a professor of financial law at the State University of Rio de Janeiro who has given evidence to Congress in Rousseff's defence. "It is a delay that has occurred in previous governments and years without any crime" being alleged.
This is true - but less money was involved. In 2001 and 2002, President Fernando Cardoso "pedaled" around US$290 million a year, at current exchange rates, according to Publica, a non-profit news agency. In 2013 Rousseff's Government "pedaled" US$10 billion and in 2014, US$15 billion (also at current rates). The practice worried Brazil's Federal Court of Accounts so much that it rejected her Government's 2014 accounts.
Some say Rousseff's actions were illegal.
"This is a credit operation prohibited by the law," said Julio de Oliveira, a public accounts prosecutor who gave evidence to the Senate's impeachment commission. "You are breaking a basic principle of public finances."
That sounds pretty serious.
It is. But the impeachment process that Rousseff is facing only applies to her current mandate - which began on January 1, 2015, after she won re-election. And after getting a sharp rap on the knuckles from the Federal Court of Accounts in April last year, the Government cleaned up its act - paying off most of its "pedaling" debts.
"As soon as the Federal Court of Accounts said it was not allowed, the Government stopped doing it," said Ribeiro.
Almost. In 2015, the Government "pedaled" around US$4 billion for a low-interest financing scheme for family farmers that it left the Bank of Brazil to pay - clearing the debt at the end of the year. Critics say Rousseff's actions contributed to Brazil losing its investment grade from ratings agencies.
"This had a huge cost," said de Oliveira. "It destroyed confidence."
Is there more?
There are six "decrees" Rousseff issued in 2015 that moved budget money around. Her accusers say that she did this without congressional approval and that this, too, is an impeachable offence. Her defence disagrees. One element of the arguments is what impact the decrees had on a requirement that the Government produce a spending surplus every year. In 2015, the Government ended up with a big deficit because it had to pay off its previous "pedaling".
The decrees involved US$27 billion at current rates, but only US$710 million of that was extra spending.
"This procedure that the president did with the decrees is extremely commonly used in Brazil," said Ribeiro.
What are the politics involved?
While experts debate the technical aspects of Rousseff's impeachment process, politically the game looks lost. That's because many Brazilians blame Rousseff for the country's deep recession and a vast corruption scandal they allege she failed to prevent. Her impeachment is a political judgment, not a juridical decision, many say, with senators acting like a jury.
And they will take all kinds of factors into account.
"To leave the economy heading not just for a recession but a depression with all its effects - for society this is very strong," said Istvan Kasznar, a professor of economic development, microeconomics and public finance at the Getulio Vargas Foundation in Rio.
