Roulette strategy is a considered plan on how to win a game of roulette. 'Win' here does not just mean getting one bet right, but rather having a profit by the time you are done staking your planned bankroll.
It is thus a lose some-win more plan.
There are numerous roulette strategies; some simple and others complex. Here's an overview of three popular roulette strategies. But, first up, a quick warm-up with definition of relevant terms;
Bankroll - The amount of money a gambler intends to spend e.g $100
Unit- The portion of the bankroll used for each bet ($100 has 20 units of $each)
Streak - The number of times a bet returns the same result (win or lose)
Session- The time it takes to spend the entire bankroll on betting
On to the strategies:

Fibonacci strategy

This strategy devised by an Italian mathematician by the same name involves combining the last two units for the next bet until you win. Once you win, you return to betting one unit and continue in the same progression until the session ends.
  • Bet $5 - Lose
  • Bet $5-Lose
  • Bet$10- Lose
  • Bet$15- win
  • Bet $5...
The $15 win helps you to recoup all your lost money. The advantage of this strategy is that you can finish a session with a profit even if you lose more bets than you win.
The downside is that a losing streak can quickly wipe out your bankroll.

Martingale strategy

This one involves doubling the number of units in the next bet after a loss. It is used in a 50/50 chance game e.g Red or black. The doubling means a single win will recover all the money lost in previous bets.
The dark side of the Martingale strategy is that it works with the gambler's fallacy that chances change after every spin. The truth is that chances remain 50/50. Investing more and more in a losing streak doesn't sound like a very clever thing to do.

Reverse Martingale strategy (Paroli)

The Paroli involves upping the ante when you win and reducing the amount you bet when you lose. In this way, a winning streak will yield big wins and a losing streak will have minimum losses.
The disadvantage of this strategy is that it takes away the risk factor by withdrawing during losses. Low risk oft means little wins. Also, the assumption of a streak does not always hold. This one is pretty superstitious.
At the end of the day, gambling is a game chance. While attempts can be made to mathematically calculate chance, no single calculation can achieve a universal working strategy. That said, some roulette strategies have proven to work better than others. These three strategies are pretty popular, but the ultimate strategy is knowing when to quit.