One-dimensional ZnO nanostructures have great potential applications in the fields of optoelectronic and sensor devices.  Therefore, it is very important to realize the controllable growth of one-dimensional ZnO nanostructures and investigate their properties. The main points for this thesis are not only to successfully realize the controllable growth of ZnO nanorods (ZNRs), ZnO nanotubes (ZNTs) and ZnMgO/ZnO heterostructures, but also investigate the structure and optical properties in detail by means of scanning electron microscope (SEM), transmission electron microscope (TEM), resonant Raman spectroscopy (RRS), photoluminescence (PL), time resolved PL (TRPL), X-ray photoelectron spectroscopy (XPS) and Secondary ion mass spectrometry (SIMS). For ZNRs, on one hand, ZNRs have been successfully synthesized by a two-step chemical bath deposition method on Si substrates. The diameter of ZNRs can be well controlled from 150 nm to 40 nm through adjusting the diameter and density of the ZnO nanoparticles pretreated on the Si substrates. The experimental results indicated that both diameter and density of ZnO nanoparticles on the substrates determined the diameter of ZNRs. But when the density is higher than the critical value of 2.3×108cm-2, the density will become the dominant factor to determine the diameter of ZNRs. One the other hand, the surface recombination of ZNRs has been investigated in detail. Raman, RRS and PL results help us reveal that the surface defects play a significant role in the as-grown sample. It is the first time to the best of our knowledge that the Raman measurements can be used to monitor the change of surface defects and deep level defects in the CBD grown ZNRs. Then we utilized TRPL technique, for the first time, to investigate the CBD grown ZNRs with different diameters. The results show that the decay time of the excitons in ZNRs strongly depends on the diameter. The altered decay time is mainly due to the surface recombination process. A thermal treatment under 500°C can strongly suppress the surface recombination channel. A simple carrier and exciton diffusion equation is also used to determine the surface recombination velocity, which results in a value between 1.5 and 4.5 nm/ps. Subsequently, we utilized XPS technique to investigate the surface composition of as-grown and annealed ZNRs so that we can identify the surface recombination centers. The experimental results indicated that the OH and H bonds play the dominant role in facilitating surface recombination but specific chemisorbed oxygen also likely affect the surface recombination. Finally, on the basis of results above, we explored an effective way, i.e. sealing the beaker during the growth process, to effectively suppress the surface recombination of ZNRs and the suppression effect is even better than a 500oC post-thermal treatment. For ZNTs, the structural and optical properties have been studied in detail. ZNTs have been successfully evolved from ZNRs by a simple chemical etching process. Both temperature-dependent PL and TRPL results not only further testify the coexistence of spatially indirect and direct transitions due to the surface band bending, but also reveal that less nonradiative contribution to the emission process in ZNTs finally causes their strong enhancement of luminescence intensity. For ZnMgO/ZnO heterostructures, the Zn0.94Mg0.06O/ZnO heterostructures have been deposited on 2 inch sapphire wafer by metal organic chemical vapor deposition (MOCVD) equipment. PL mapping demonstrates that Mg distribution in the entire wafer is quite uniform with average concentration of ~6%. The annealing effects on the Mg diffusion behaviors in Zn0.94Mg0.06O/ZnO heterostructures have been investigated by SIMS in detail. All the SIMS depth profiles of Mg element have been fitted by three Gaussian distribution functions. The Mg diffusion coefficient in the as-grown Zn0.94Mg0.06O layer deposited at 700 oC is two orders of magnitude lower than that of annealing samples, which clearly testifies that the deposited temperature of 700 oC is much more beneficial to grow ZnMgO/ZnO heterostructures or quantum wells. This thesis not only provides the effective way to fabricate ZNRs, ZNTs and ZnMgO/ZnO heterostructures, but also obtains some beneficial results in aspects of their optical properties, which builds theoretical and experimental foundation for much better understanding fundamental physics and broader applications of low-dimensional ZnO and related structures. / Endimensionella nanostrukturer av ZnO har stora potentiella tillämpningar för optoelektroniska komponenter och sensorer. Huvudresultaten för denna avhandling är inte bara att vi framgångsrikt har realiserat med en kontrollerbar metod ZnO nanotrådar (ZNRs), ZnO nanotuber (ZNTs) och ZnMgO/ZnO heterostrukturer, utan vi har också undersökt deras struktur och optiska egenskaper i detalj. För ZNRs har diametern blivit välkontrollerad från 150 nm  ner till 40 nm. Den storlekskontrollerande mekanismen är i huvudsak relaterad till tätheten av ZnO partiklarna som är fördeponerade på substratet. De optiska mätningarna ger upplysning om att ytrekombinationsprocessen spelar en betydande roll för tillväxten av ZNR. En värmebehandling i efterhand  vid 500 grader Celsius eller användande av en förseglad glasbägare under tillväxtprocessen kan starkt hålla nere kanalerna för ytrekombinationen.För ZNT, dokumenterar vi inte bara samexistensen av rumsliga indirekta och direkta  övergångar på grund av bandböjning, men vi konstaterar också att vi har mindre icke-strålande bidrag till den optiska emissionsprocessen i ZNT. För ZnMgO/ZnO heterostrukturer konstaterar vi med hjälp av analys av Mg diffusionen i den växta och den i efterhand uppvärmda Zn(0.94)Mg(0.06)O filmen, att en tillväxt vid 700 grader Celsius är den mest lämpliga för att växa ZnMgO/ZnO heterostrukturer eller kvantbrunnar.   Denna avhandling ger en teoretisk och experimentell grund för bättre förståelse av grundläggande fysik och för tillämpningar av lågdimensionella strukturer. / SSF, VR