Metal-organic frameworks (MOFs) are an emerging class of hybrid molecular materials with extended structures constructed from inorganic metal nodes/ions interconnected with multidentate organic linkers. They have been explored in a broad range of applications owing to their modular nature. However, MOFs suffer from restricted diffusion of substrates and products through relatively small channels. To overcome diffusional limitation, our group recently reduced the thickness of one dimension of MOFs to a monolayer to afford a new class of hybrid materials, metal-organic layers (MOLs). This dissertation focuses on the development of new MOFs and MOLs for sensing and catalytic applications. The first part (Chapter 1) of this dissertation focuses on rational design of MOFs for oxygen sensing. We developed a novel strategy of using mixed ligands of very different chemical nature to construct functional MOFs. Using this method, we synthesized a phosphorescence/fluorescence dual-emissive nanoscale metal-organic framework (nMOF) as an intracellular oxygen sensor. The nMOF contains a Pt(II)-porphyrin ligand as an O2-sensitive probe and a Rhodamine-B isothiocyanate (RITC) ligand as an O2-insensitive reference probe, and exhibits good crystallinity, high stability, and excellent ratiometric luminescence response to O2 partial pressure. In vitro experiments confirmed the applicability of this nMOF as an intracellular O2 biosensor. The second part (Chapter 2-4) of the dissertation reports the synthesis of functional MOLs as novel single-site solid catalysts for a variety of organic transformations. MOLs overcome xxi substrate size and diffusion limitations often seen in MOFs owing to their unique monolayer structures. We demonstrated the superior performance of MOLs over MOFs in many catalytic reactions. In Chapter 2, we incorporated Ru(bpy)32+ photosensitizer into BPY-MOL via post synthetic metalation to afford photoactive RuBPY-MOL. RuBPY-MOL exhibits higher efficacy than RuUiO-67 in multicomponent photoreactions such as intramolecular and crossed [2+2] photocyclization of bis(enones) and photocatalytic Meerwein addition reactions. In Chapter 3, we report the synthesis of IrBPY-MOL containing cyclometalated iridium complex. IrBPY-MOL was an efficient catalyst for photopolymerization of methyl methacrylate (MMA), benzyl methacrylate (BnMA) and tert-butyl methacrylate (tBuMA). The resulting polymers possessed high-number average molar masses and low polydispersity indices. We also showed that IrBPY-MOL significantly outperformed IrUiO-69 MOF. In Chapter 4, we immobilized enantiopure pybox ligand onto the SBUs of MOLs through ligand exchange. The resultant pybox-MOLs functioned as heterogeneous asymmetric catalysts of A3-coupling reaction (aldehyde-alkyne-amine) in good yields and high enantioselectivities.