Meeting global demand of safe and healthy food for the ever-increasing population now and into the future is currently a crucial challenge. Increasing crop production by preserving environment and mitigating climate change should thus be the main goal of today’s agriculture. Conventional farming is characterized by use of high-yielding varieties, irrigation water, chemical fertilizers and synthetic pesticides to increase yields. However, due to either over- or misuse of chemical fertilizers or pesticides in many agro-ecosystems, such farming is often blamed for land degradation and environmental pollution and for adversely affecting the health of humans, plants, animals and aquatic ecosystems. Of all inputs required for increased agricultural production, nutrients are considered to be the most important ones. Organic farming, with use of organic sources of nutrients, is proposed as a sustainable strategy for producing safe, healthy and cheaper food and for restoring soil fertility and mitigating climate change. However, there are several myths and controversies surrounding the use of organic versus inorganic sources of nutrients. The objectives of this paper are: (i) to clarify some of the myths or misconceptions about organic versus inorganic sources of nutrients and (ii) to propose alternative solutions to increase on-farm biomass production for use as organic inputs for improving soil fertility and increasing crop yields. Common myths identified by this review include that organic materials/fertilizers can: (i) supply all required macro- and micro-nutrients for plants; (ii) improve physical, chemical and microbiological properties of soils; (iii) be applied universally on all soils; (iv) always produce quality products; (v) be cheaper and affordable; and (vi) build-up of large amount of soil organic matter. Other related myths are: “legumes can use entire amount of N2 fixed from atmosphere” and “bio-fertilizers increase nutrient content of soil.” Common myths regarding chemical fertilizers are that they: (i) are not easily available and affordable, (ii) degrade land, (iii) pollute environment and (iv) adversely affect health of humans, animals and agro-ecosystems. The review reveals that, except in some cases where higher yields (and higher profits) can be found from organic farming, their yields are generally 20–50% lower than that from conventional farming. The paper demonstrates that considering the current organic sources of nutrients in the developing countries, organic nutrients alone are not enough to increase crop yields to meet global food demand and that nutrients from inorganic and organic sources should preferably be applied at 75:25 ratio. The review identifies a new and alternative concept of Evergreen Agriculture (an extension of Agroforestry System), which has potential to supply organic nutrients in much higher amounts, improve on-farm soil fertility and meet nutrient demand of high-yielding crops, sequester carbon and mitigate greenhouse gas emissions, provide fodder for livestock and fuelwood for farmers and has potential to meet global food demand. Evergreen Agriculture has been widely adapted by tens of millions of farmers in several African countries and the review proposes for evaluation and scaling-up of such technology in Asian and Latin American countries too.