Exoplanet hunting efforts have revealed the prevalence of exotic worlds with diverse properties, including Earth-sized bodies, which has fueled our endeavor to search for life beyond the Solar System. Accumulating experiences in astrophysical, chemical, and climatological characterization of uninhabitable planets are paving the way to characterization of potentially habitable planets. In this paper, we review our possibilities and limitations in characterizing temperate terrestrial planets with future observational capabilities through the 2030s and beyond, as a basis of a broad range of discussions on how to advance astrobiology with exoplanets. We discuss the observability of not only the proposed biosignature candidates themselves but also of more general planetary properties that provide circumstantial evidence, since the evaluation of any biosignature candidate relies on its context. Characterization of temperate Earth-sized planets in the coming years will focus on those around nearby late-type stars. The James Webb Space Telescope (JWST) and later 30-meter-class ground-based telescopes will empower their chemical investigations. Spectroscopic studies of potentially habitable planets around solar-type stars will likely require a designated spacecraft mission for direct imaging, leveraging technologies that are already being developed and tested as part of the Wide Field InfraRed Survey Telescope (WFIRST) mission. Successful initial characterization of a few nearby targets will be an important touchstone toward a more detailed scrutiny and a larger survey that are envisioned beyond 2030. The broad outlook this paper presents may help develop new observational techniques to detect relevant features as well as frameworks to diagnose planets based on the observables. Key Words: ExoplanetsBiosignaturesCharacterizationPlanetary atmospheresPlanetary surfaces. Astrobiology 18, 739-778. Table of Contents 1.Introduction 2.From Astrophysical Characterization to Astrobiological Characterization 2.1.The era of astrophysical characterization of exoplanets 2.2.The era of chemical characterization of exoplanets 2.3.The era of astrobiological characterization of exoplanets 3.Characterizing Transiting Planets 3.1.Astrophysical characterization 3.1.1.Method and sensitivity 3.1.2.Opportunities through 2030 3.2.Chemical/Climatological characterization: Transmission spectroscopy 3.2.1.Method and sensitivity 3.2.2.What can be studied? 3.2.3.Opportunities through 2030 3.3.Chemical/Climatological characterization: Eclipse spectroscopy 3.3.1.Method and sensitivity 3.3.2.What can be studied? 3.3.3.Opportunities through 2030 4.Characterizing Planets with General Orbital Inclination 4.1.Astrophysical characterization 4.1.1.Methods and sensitivity 4.2.Chemical/Climatological characterization: Phase curves 4.2.1.Method and sensitivity 4.2.2.What can be studied? 4.2.3.Opportunities through 2030 4.3.Chemical/Climatological characterization: High-contrast imaging 4.3.1.Method and sensitivity 4.3.2.What can be studied? 4.3.3.Opportunities through 2030 4.4.Chemical/Climatological characterization: Spectral separation 4.4.1.Method and sensitivity 4.4.2.What can be studied? 4.4.3.Opportunities through 2030 5.Contextual Information 5.1.Properties of the host star 5.1.1.Mass, radius, SED in the visible/IR range 5.1.2.Activity (SED in UV, X-ray, superflares) 5.2.Orbital architecture of the planetary system 5.3.Characterization of larger planets in the system 6.Prospects Beyond 2030 6.1.Mission concepts currently being studied in the United States 6.1.1.Habitable Exoplanet Imaging Mission (HabEx) 6.1.2.Large UltraViolet Optical and InfraRed surveyor (LUVOIR) 6.1.3.Origins Space Telescope (OST) 6.2.Ideas for the far future 6.2.1.Direct imaging in the mid-IR 6.2.2.ExoEarth Mapper 6.2.3.Telescope on the Moon 6.2.4.One-hundred-meter-class ground-based telescope 7.Summary: Ideal Timeline Acknowledgments Author Disclosure Statement References 765