All organisms are defined by the sequence of letters that make up their DNA. Change the code of the DNA, and you create different characteristics or create a different organism. Organisms can be copied (cloning of cells having been done for a long time, cloning of a mammal the first time in 1996, and it is so mainstream today that if you live in the US, you almost certainly have eaten cloned plants and have probably eaten food from cloned animals), changed (gene editing, gene deletion, gene silencing, gene addition, gene therapy, etc., such as genetic conditions cured by gene therapy starting in about 2006), or created from scratch (manufacture an artificial genome and create a living cell, done in 2010). This is very well established these days and is no more a theory than computer programming, electronics, or automobile mechanics are theories. It is used in practice in the fields of biology and agriculture every day.
A 747 probably would have seemed like unfathomable magic in 500 BC, but today, a 747 (although still awesome) isn't considered mysterious or controversial.
The workings of DNA and organisms are going from being mysterious and unknown to being (although still awesome) increasingly well understood, with that understanding increasingly allowing purposeful modification and engineering.
This is the field I work in currently -- synthesizing DNA -- and many of our customers are at the cutting edge of synthetic biology.