Methods of making alkyl esters are described herein. The methods are capable of using raw, unprocessed, low-cost feedstocks and waste grease. Generally, the method involves converting a glyceride source to a fatty acid composition and esterifying the fatty acid composition to make alkyl esters. In an embodiment, a method of making alkyl esters comprises providing a glyceride source. The method further comprises converting the glyceride source to a fatty acid composition comprising free fatty acids and less than about 1% glyceride by mass. Moreover, the method comprises esterifying the fatty acid composition in the presence of a solid acid catalyst at a temperature ranging firm about 70° C. to about 120° C. to produce alkyl esters, such that at least 85% of the free fatty acids are converted to alkyl esters. The method also incorporates the use of packed bed reactors for glyceride conversion and/or fatty acid esterification to make alkyl esters.