Inorganic compounds generally do not have C-H bonds, while organic compounds do have such bonds. The distinction between inorganic and organic chemistry, however, is far from absolute.
An "inorganic compound" is technically defined as a chemical substance based on or primarily consisting of some other element than carbon. It is the antonym of an "organic substance", which is a substance that is primarily based on carbon, which along with hydrogen and oxygen, comprises 93% of the "biomass" of the Earth, providing a natural dividing line between chemicals generally of interest in "life sciences", and those of interest elsewhere.
Inorganic chemistry, therefore, is "the sub-discipline of the field of chemistry that studies interactions, reactions, and substances primarily involving elements other than carbon".
This definition would seem to create a disproportionate divide in favor of inorganic chemistry over organic, given that there are 117 other known or theorized elements besides carbon, 83 of which are "primordial elements" stable enough to have been around before the formation of the Earth. However, the versatility and flexibility of carbon in forming a wide array of diverse molecules, and the disproportionate number of sub-fields pursued in modern chemistry that are interested in organic substances tend to balance the scales or even tip the balance toward organic chemistry.
In addition, the inclusion in both disciplines of molecules based on carbon, but including other elements that react in unique ways, blurs the dividing line between the substances of primary interest to both fields. While 93% of the mass of a human is hydrogen, carbon, and oxygen, the remaining 7% consists of almost 60 other elements, of which about 20 are considered essential for human life. Among the most important are nitrogen, calcium, sodium, potassium, chlorine, sulfur, phosphorous, iron, copper, and zinc.
Of particular interest to both fields is organometallics, a class of chemicals in which a metal is bound to a carbon atom. The properties of the metal (very often the ability to exist in several oxidation states, as with iron or zinc) can be leveraged in combination with the properties of the organic functional group in biochemical reactions ranging from organic synthesis (the organometallic will often deposit its organic functional group onto a larger molecule, often in exchange for a simpler moiety such as an oxygen or hydroxyl group) to drug interaction mechanisms (the method by which the drug exhibits its desirable behavior, often by complexing with a cellular mechanism such as a neuroreceptor to activate or disable it).