Iridates have attracted considerable interest in the last few years due to their potential to host novel electronic and magnetic phases mediated by the combination of strong spin orbit coupling and electronic correlations. Layered honeycomb lattice iridates A_2IrO_3 (A =Na, Li) have been proposed as candidate materials for the realization of the highly frustrated Kitaev interaction as well as correlated topological insulator phases. In this thesis honeycomb iridates and rhodate (Li_2RhO_3) are experimentally investigated. Firstly, synthesis procedure, structural, magnetic, electrical and thermodynamic properties of the very well ordered honeycomb iridates and rhodate are reported including challenges faced due to disorder. Magnetic and electronic structures are also reported which were investigated using different scattering experiments and band structure calculations with the help of different international collaborators. Though both honeycomb iridates were proposed for Kitaev spin liquid state, bulk and microscopic investigation confirmed long range magnetic ordering below 15 K having zigzag and spiral magnetic structure for Na- and Li-system respectively. They also show novel spin-orbit Mott insulting state as proposed for iridates. Experimental investigations of honeycomb iridates raise many questions on the proposed spin Hamiltonians for these systems. To understand magnetic exchange in honeycomb iridates isoelectronic doping at A-site and nonmagnetic dilution at magnetic Ir-site were performed which clearly suggested very different magnetic exchanges in both the systems. Possible spin models for both of these systems are suggested from the comparison of the different proposed models with the experimental evidences. The Honeycomb rhodate Li_2RhO_3 which shows spin glass freezing at low temperature, hints degenerate magnetic ground state and possibility to find a spin liquid state. This thesis is one of the earliest investigations of the proposed Honeycomb lattice spin-orbit materials which can host Kitaev physics.