Trading algorithms are systematic rules for generating buy/sell signals based on market data and automatically executing trades. They range from simple (buy when 50-day MA crosses 200-day MA) to complex (ML models predicting price movement from microstructure data). Algorithmic trading removes emotion, enables 24/7 trading, and allows testing before deploying capital. Development involves: signal generation (what should I trade?), backtesting (did this work historically?), live trading (does this work in reality?), and risk management (how do I not blow up?).