Quantum Integrated Photonics (QIP) harnesses quantum-states of light on tiny chips, from generation to processing and eventual detection. Within this context, this thesis explores functional QIP elements resulting from the monolithic integration of semiconductor quantum dots (QDs) in tailored photonic crystal systems of coupled cavities and waveguides. QDs present atom-like optical and electronic properties, which make them ideal for a deterministic, on-demand generation of single photons. Such QD-based devices can be expected to provide solutions for applications of QIP in quantum computing, communication and metrology. Here, we exploit the pyramidal site-controlled QD technology to reproducibly fabricate quantum photonic elements in which an arbitrary number of QD quantum emitters are embedded in photonic crystal (PhC) structures with alignment precision better than 50nm. Systematic investigation of reference structures with dense arrays of QDs to observe optical mode structures, and identical structures with only a few QDs for selective excitation and coupling to prescribed modes, is conducted using spatially-resolved micro-photoluminescence spectroscopy. Observations are consolidated by quantitative comparisons to 2D FDM numerical simulations. First, defect-potential PhC cavities are made by precise transverse shifts of selected holes in a PhC defect waveguide. In these structures, defect modes confined by a local mismatch in the photonic dispersion are observed, with peculiar polarization signatures. The fundamental defect modes display quality factors and mode volumes on par with conventional Ln=3 cavities. Defect modes can be selectively excited, and weak coupling of a single QD to cavity modes is demonstrated using thermal tuning. Next, tilted-potential PhC cavities supporting Airy-Bloch photonic modes are realized by staggered shifts of holes from 0 to smax along the axis. Such modes are suitable for local interaction and extraction of single photons from site-controlled QDs and their transmission to remote locations. Selective excitation of several modes with properly positioned QDs is demonstrated. Weak coupling of a QD to a single mode is achieved by thermal tuning, showing features of Purcell effect. The quasi linear energy-position dispersion of the Airy-Bloch modes maxima provides a mean for constructing an efficient wavelength-multiplexed single-photon injector. Finally, a monolithic model structure, consisting of two PhC waveguides side-coupled to a center Ln=3 cavity, with four ports connected to suspended nanobeams and grating couplers for light extraction/injection, is fabricated and tested. Five QDs are embedded in specific positions; four can act as on-chip single photon sources while the fifth, embedded in the center cavity, could be used for photon processing functions. The quasi-resonant excitation of this fifth QD via its p-shell is demonstrated using a pump laser beam that is injected into a waveguide through the grating coupler. Part of the s-shell emission is coupled to another targeted optical channel, demonstrating a complete photonic connectivity of all elements, a fundamental requirement towards on-chip processing. The results of this thesis consolidate the assets of the site-controlled pyramidal QD technology and tailored PhC confinement towards the realization of functional elements for quantum integrated photonics circuits.