Primary mission objectives included the deployment of the Navy's Syncom IV-F5 defense communications satellite (also known as LEASAT-5) and the retrieval of NASA's Long Duration Exposure Facility (LDEF) placed in Earth orbit in 1984. Syncom IV-F5 was the last in a series of five Navy satellites designed to provide worldwide, high-priority communications between aircraft, ships, submarines and land-based stations for the U.S. military services and the Presidential Command Network. LDEF was a research satellite that contained experiments ranging in interest from medicine to materials to astrophysics.

Life sciences payloads on board STS-32 included the Characterization of Neurospora Circadian Rhythms (CNCR) experiment. Many animal and plant processes on Earth are regulated by an internally generated rhythm of about 24 hours. This rhythm may be affected by many environmental factors, such as light and gravity. The CNCR experiment was designed to investigate the circadian rhythms of the pink bread mold, Neurospora crassa, in the absence of geophysical and environmental cues in microgravity.

Several Detailed Supplementary Objectives (DSOs) were also performed during the STS-32 mission. A DSO is a NASA-sponsored investigation performed by Space Shuttle crewmembers, who serve as the test subjects. These studies required minimal crew time, power and stowage. Biomedical DSOs focus on operational concerns, including space motion sickness, cardiovascular deconditioning, muscle loss, changes in coordination and balance strategies, radiation exposure, pharmacokinetics and changes in the body's biochemistry.

Additional payloads included Protein Crystal Growth (PCG) designed to grow large, high-quality crystals for medical research and drug development, Fluid Experiment Apparatus (FEA) for materials processing research, American Flight Echocardiograph (AFE) to provide inflight measurements of the size and functioning of the heart, Latitude/Longitude Locator (L3) to determine the exact location of oceanographic features on Earth from the Shuttle, Mesoscale Lightning Experiment (MLE) to investigate the global distribution and relationship between lightning events, IMAX Cargo Bay Camera to document space flight activities, and Air Force Optical Site (AMOS) experiment to collect imagery and signature data on the Shuttle from a location in Hawaii.

The STS-32 mission came to an end on January 20, 1990, as the Space Shuttle Columbia landed at Edwards Air Force Base in California. This was the 3rd night landing in the Space Shuttle Program's history.