Since the time of their discovery in the 1960s, transition metal carbenes have fascinated chemists and been the subject of much research interest. Carbenes have traditionally been divided up into two classes, both named after the chemists who initially discovered them. Fischer carbenes, which were discovered in 1964 by E.O. Fischer, are more associated with mid-to-late transition metals in low-oxidation states. They are considered to be electrophilic and bear stabilizing heteroatoms such as oxygen, nitrogen, or sulfur as substituents. Schrock carbenes, which were discovered by Richard Schrock in 1974, are often associated with early transition metals in high-oxidation states. They are considered to be nucleophilic in nature and usually contain alkyl or hydrogen substituents on the carbene. For this reason, they are often referred to as alkylidenes. However, many examples of transition metal carbenes fall outside of these classical descriptions and chemists have discovered that the electronics and reactivity of the M à C interaction depend on many different factors including choice of metal, substituents at the carbene carbon, oxidation state, coordination number, and the nature of the supporting ligands.The purpose of this work is to expand our knowledge of transition metal carbenes, particularly those of the Group 10 triad. To that end, a ligand containing a tethered alkyne moiety was designed with the goal of synthesizing untethered four-coordinate carbenes and a fundamental study of its coordination chemistry toward Group 10 metals in different oxidation states was carried out. Reactions of a low-valent nickel complex of this ligand toward diazo and organoazide reagents were attempted, however, desired carbene and nitrene species proved elusive. Additionally, an untethered electrophilic carbene was targeted and ultimately yielded an η1-N "end-bound" diazo complex of Pt(II). Utilizing a different supporting ligand, a series of three-coordinate platinum benzylidene derivatives and a platinum alkylidene were synthesized. These compounds represent the first examples of benzylidenes on a platinum center and the first example of any late transition metal alkylidene. Due to the detection of straightforward decomposition pathways, a thorough study of their thermal stability was carried out and their decomposition products were characterized. Several reactions were carried out, demonstrating 1,2-addition of E-H bonds (E = Cl, O) across the M=C linkage, as well as [2+2] cycloadditions. Finally, the reverse reaction of a decomposition pathway involving β-hydrogen containing carbenes was studied and several pieces of evidence consistent with the formation of a carbene intermediate at elevated temperatures from metal-olefin starting materials is presented.