Natural extracts are the source of many antioxidant substances. They have proven useful not only as supplements preventing diseases caused by oxidative stress and food additives preventing oxidation but also as system components for the production of metallic nanoparticles by the so-called green synthesis. This is important given the drastically increased demand for nanomaterials in biomedical fields. The source of ecological technology for producing nanoparticles can be plants or microorganisms (yeast, algae, cyanobacteria, fungi, and bacteria). This review presents recently published research on the green synthesis of nanoparticles. The conditions of biosynthesis and possible mechanisms of nanoparticle formation with the participation of bacteria are presented. The potential of natural extracts for biogenic synthesis depends on the content of reducing substances. The assessment of the antioxidant activity of extracts as multicomponent mixtures is still a challenge for analytical chemistry. There is still no universal test for measuring total antioxidant capacity (TAC). There are many in vitro chemical tests that quantify the antioxidant scavenging activity of free radicals and their ability to chelate metals and that reduce free radical damage. This paper presents the classification of antioxidants and non-enzymatic methods of testing antioxidant capacity in vitro, with particular emphasis on methods based on nanoparticles. Examples of recent studies on the antioxidant activity of natural extracts obtained from different species such as plants, fungi, bacteria, algae, lichens, actinomycetes were collected, giving evaluation methods, reference antioxidants, and details on the preparation of extracts.