This dissertation is devoted to the study of fuzzy modal logics that formalise (paraconsistent) reasoning about uncertainty. The understanding of ‘uncertain information (data)’ here includes any combination of the following three characteristics. First, the information can be graded, i.e., the statement is equipped with a~\emph{truth degree} rather than a~\emph{truth value}. Second, the information can be incomplete. Third, the information can be contradictory. All the logics in question can be divided into two kinds. First, the more ‘traditional’ modal logics defined on $[0,1]$-valued Kripke models (possibly, with fuzzy accessibility relations) whose language includes modal operators $\Box\phi$ and $\lozenge\phi$ interpreted as, respectively, infima and suprema of $\phi$'s values in the accessible states. The second kind of logics contains so-called ‘two-layered’ logics. In this framework, the language is divided into three parts: the \emph{inner layer} $\mathscr{L}_i$, the \emph{outer layer} $\mathscr{L}_o$ and the \emph{non-nesting modality} $\mathsf{M}$. The idea is to use $\mathscr{L}_i$ to \emph{describe events}, interpret $\mathsf{M}$ as a~\emph{measure on the set of events} (e.g., as a~probability function, belief function, plausibility, etc.) corresponding to the degree of the agent's (un)certainty in a~given event, and then \emph{reason about} this (un)certainty in $\mathscr{L}_o$. A \emph{frame} in a~two-layered logic is, thus, a~set with a~measure defined thereon. These two kinds of logics correspond to two ways of interpreting uncertainty. In the less formal one that is closer to the intuitive understanding of constructions such as ‘I believe’, ‘I~am certain that’, etc., we will be using the logics with the Kripke-frame semantics. In the more formal case where the degree of one's certainty or belief in $\phi$ is assumed to behave as a~concrete uncertainty measure, we will use the two-layered logics. The logics studied in the manuscript can be also divided into ‘qualitative’ and ‘quantitative’ ones depending on the operations the agent is supposed to be able to carry out with their degree of certainty in $\phi$. In the qualitative case, the agent is only supposed to be capable of comparison of their degrees of certainty in different statements (e.g., ‘I am more certain that it is going to snow today than that there is going to be a~hailstorm’) or state their complete certainty or disbelief therein (e.g., ‘I am completely sure that it is not going to rain’). In other words, the agent does not know the exact numerical value of their certainty. In contrast to that, in the quantitative case, the agent is supposed to know this value, whence, they are able to conduct some basic arithmetic operations with them: e.g., addition or subtraction. The logics formalising quantitative reasoning will thus be based on the Łukasiewicz logic and its expansions as it can express the arithmetic operations. The logics for the quantitative reasoning, in their turn, will use G\"{o}del logic as its propositional fragment. We will mainly focus on providing the axiomatisations for the logics formalising reasoning about uncertainty, establishing their complexity evaluations and devising decision procedures as well as on investigating their semantical properties. Among those, we will be mostly concerned with the correspondence between formulas and the classes of frames they define, and faithful translations and embeddings of the logics into one another.