The future will bring changes in energy production and consumption that will affect the performance of electricity distribution networks. Electric vehicle charging will increase consumption; the installation of solar photovoltaic (PV) units will increase production. Both will change the energy flow and affect the power quality. The installation of solar PV units or electric vehicle (EV) charging has a limit above, which they unacceptably deteriorate the distribution networks' performance. This limit is referred to as the hosting capacity of the distribution network. This work is about developing, applying and studying methods for estimating the hosting capacity, especially solar PV. Three fundamentally different methods to estimate solar PV hosting capacity for single-phase and three-phase units have been identified by a detailed review of the literature:  deterministic, stochastic and time-series. The methods were shown to differ in the required input data, accuracy, computation time, consideration of uncertainties, and time-correlation between different phenomena. The methods have also been compared in relation to their application for the assessment of connection requests (screening) or detailed analysis. Solar power production, energy consumption and distribution networks’ all have uncertainties associated with them. It is helpful to distinguish between two types of uncertainties when estimating the hosting capacity: aleatory (“certain”) and epistemic (“uncertain”) uncertainties. A stochastic approach, ‘mixed aleatory-epistemic’, was applied to about 1500 low-voltage distribution networks. A similar stochastic approach and models were applied to estimate low-voltage networks' hosting capacity for electric vehicle charging. A deterministic method was applied to determine the hosting capacity considering the thermal overload phenomenon for both PV and EV charging. A planning risk has been introduced to quantify the risk of the distribution network not being able to cope with a future penetration of solar PV or EV charging. The planning level entails that a distribution network operator accepts a certain risk of exceeding the overvoltage limit. The concept has been applied as part of the stochastic approach. The hosting capacity for a distribution network is quantified considering a performance index and a limit to what is an acceptable deterioration of that index. The 90th percentile of the annual peak demand (overvoltage or overload) has been used as a performance index in most of the hosting capacity studies in this work. The time-of-day (ToD) and time-of-year (ToY) concepts were introduced to model the aleatory uncertainties. The time-of-day exemplifies the relevant part of the day, and the time-of-year shows the parts of the year applicable for hosting capacity studies when high solar power production can be expected. The time-of-day of 10 am to 2 pm has been applied. The period from 21st March to 21st September was the applied time-of-year. The latter two, ToD and ToY, need to be defined for the application of the concept to other areas than those covered in this work. It was shown that the hosting capacity would be underestimated by about 10% if an incorrect ToD were used. Voltage magnitude and solar power production measurements, over one year with a 10-minute resolution, were obtained for thirty-three 10/0.4 kV distribution transformers in Northern Sweden. A method of obtaining the ‘background voltage’ from the measurements was formulated. The background voltage (including its uncertainties) was one of the factors with the greatest influence on the hosting capacity.  Stochastic models for distribution networks were built, and the hosting capacity for low voltage distribution networks has been studied. The outcome shows that three-phase solar PV units have a higher hosting capacity than single-phase units. The model and method developed can be used as a planning tool by distribution network operators (DSOs). The inclusion of the uncertainties and correct handling of planning risks is paramount for decision making by DSOs. The results show that background voltage variations should be considered from measurements, and appropriate ToD/ToY should be used. The quantification of the hosting capacity requires both consumption and voltage measurements in the distribution networks.  The work has also shown that the time of the day and year (ToD and ToY) need to be considered for the many hosting capacity methods. The impact is expected to be highest in the ToD and ToY. Also, the two types of uncertainties have been clarified in this work. They need to be considered as the decisions DSOs make will depend on them. This work has generally found that hosting capacity estimation methods are many and different. They are all applicable and useful tools for identifying the factors in distribution networks that can hold up solar PV and EV charging penetration. It has also been found that there is a strong link between distribution network planning and hosting capacity estimation methods. The hosting capacity methods in this work can undertake the risks connected to solar PV and EV charging.