Nowadays, the classical pulmonary artery catheter (PAC) has an almost 50-year-old history of its clinical use for hemodynamic monitoring. In recent years, the PAC evolved from a device that enabled intermittent cardiac output measurements in combination with static pressures to a monitoring tool that provides continuous data on cardiac output, oxygen supply and-demand balance, as well as right ventricular (RV) performance. In this review, which consists of two parts, we will introduce the difference between intermittent pulmonary artery thermodilution using cold bolus injections, and the contemporary PAC enabling continuous measurements by using a thermal filament which at random heats up the blood. In this first part, the insertion techniques, interpretation of waveforms of the PAC, the interaction of waveforms with the respiratory cycle and airway pressure as well as pitfalls in waveform analysis are discussed. The second part will cover the measurements of the contemporary PAC including measurement of continuous cardiac output, RV ejection fraction, end-diastolic volume index, and mixed venous oxygen saturation. Limitations of all of these measurements will be highlighted there as well. We conclude that thorough understanding of measurements obtained from the PAC are the first step in successful application of the PAC in daily clinical practice.